Steven L. Lane, Attorney, Appellate Section, Criminal Division, United States Department of Justice, with whom Michael J. Sullivan, United States Attorney, George W. Vien and John A. Wortmann, Jr., Assistant United States Attorneys, were on brief, for appellee.

Before SELYA, LYNCH and LIPEZ, Circuit Judges.

SELYA, Circuit Judge.

This is a landmark case; for the first time in its history, this court must review a sentence of death imposed by a federal judge. To that extent, we are writing on a pristine page. We are guided in this pathbreaking endeavor, however, by a variety of reliable sources, including Supreme Court precedent, decisions of other courts of appeals in capital cases, and legal principles of general application.

With this brief preface, we turn to the particulars of the case at hand. Defendant-appellant Gary Lee Sampson entered a guilty plea to two counts of carjacking resulting in death. See 18 U.S.C. § 2119(3). On January 29, 2004, the district court sentenced Sampson to death on the recommendation of a jury of his peers.

Sampson's appeal from his sentence raises a host of claims. The first six include five claims that contest the constitutionality of the Federal Death Penalty Act, 18 U.S.C. §§ 3591-3598 (FDPA), pursuant to which the district court pronounced sentence, and one that contests the constitutionality of the death penalty in general. There follows a litany of claims concerning alleged errors specific to Sampson's penalty-phase trial. The district court's rulings on many of these issues are embodied in a series of published opinions. See United States v. Sampson, 335 F.Supp.2d 166 (D.Mass.2004) (Sampson IV); United States v. Sampson, 332 F.Supp.2d 325 (D.Mass.2004) (Sampson III); United States v. Sampson, 275 F.Supp.2d 49 (D.Mass.2003) (Sampson II); United States v. Sampson, 245 F.Supp.2d 327 (D.Mass.2003) (Sampson I).

We begin this opinion by sketching the background of the case. We then discuss Sampson's arguments about the constitutionality of the FDPA and the death penalty itself. Finally, we address the myriad claims of trial-related error. In the end, we reject Sampson's asseverational array in its entirety and affirm his capital sentence.

I. BACKGROUND

We briefly recount the facts underlying Sampson's claims. Many of these facts are rehearsed in Sampson IV, 335 F.Supp.2d at 174-75, and McCloskey v. Mueller, 446 F.3d 262, 264-65 (1st Cir. 2006), and we assume the reader's familiarity with those opinions.

Sampson committed a series of bank robberies in North Carolina in May, June, and July of 2001. He then fled to Massachusetts. On July 23, he called the FBI's Boston office and offered to self-surrender. The call was disconnected and, although he waited for the police to arrive, Sampson was not apprehended.

The next day, Phillip McCloskey, a 69-year-old retiree, was driving his car in Weymouth, Massachusetts. He picked up Sampson, who was hitchhiking. When McCloskey later tried to drop Sampson off, Sampson pulled out a knife and told McCloskey to keep driving. Once they reached Marshfield, Sampson forced McCloskey out of the car and attempted to restrain him with a belt. When McCloskey resisted, Sampson stabbed him multiple times and then slit his throat, nearly decapitating him. Sampson proceeded to steal McCloskey's money and tried to steal his car, which would not start.

Three days later, Jonathan Rizzo, a 19-year-old college student, picked up Sampson (who was posing as a stranded traveler) along a road in Plymouth. Sampson forced Rizzo at knifepoint to drive to Abington, where Sampson maintained a makeshift campsite. Sampson tied Rizzo to a tree, gagged him with a sock and a bandana, stabbed him repeatedly in the neck and chest, and slit his throat. After Rizzo was dead, Sampson stole his car and drove to New Hampshire.

On July 29, Sampson broke into a home on Lake Winnipesaukee. The next day, the caretaker (Robert Whitney) arrived. Sampson tied him to a chair, gagged him with a washcloth, and strangled him to death with a rope. Sampson then appropriated Whitney's car and drove to Vermont.

On July 31, William Gregory picked up Sampson, who was hitchhiking, near West Bridgewater, Vermont. Sampson attempted to force Gregory at knifepoint onto a dirt road so that he could tie him to a tree and steal his car. Gregory, however, pulled into a rest area and escaped on foot. Sampson made off with Gregory's car. Later that day, he broke into a home near the Killington ski area. He then called 911 and offered to turn himself in for carjacking Gregory and for the earlier bank robberies. Vermont state troopers arrested Sampson at that locus. Following his detention, Sampson waived his Miranda rights, see Miranda v. Arizona, 384 U.S. 436, 444-45, 86 S.Ct. 1602, 16 L.Ed.2d 694 (1966), and made several detailed confessions to the authorities.

On October 24, 2001, a federal grand jury charged Sampson with two counts of carjacking resulting in death (namely, the murders of McCloskey and Rizzo). Sampson offered to plead guilty in exchange for a sentence of life imprisonment without parole but that overture was rejected.

In short order, the government filed a superseding indictment to comply with Ring v. Arizona, 536 U.S. 584, 609, 122 S.Ct. 2428, 153 L.Ed.2d 556 (2002), and then served a notice of intent to seek the death penalty, see 18 U.S.C. § 3593(a). After filing numerous pretrial motions that unsuccessfully challenged the constitutionality of the FDPA, Sampson eventually entered a guilty plea to both counts of the superseding indictment.

The district court empaneled a death-qualified jury to determine what punishment should be imposed. See id. § 3593(b)(2)(A); see also United States v. Green, 407 F.3d 434, 436-37 (1st Cir.2005) (discussing "death-qualified" jury requirement). On December 23, 2003, after a six-week penalty-phase trial conducted in accordance with the FDPA, the jury unanimously recommended that Sampson be sentenced to death on both counts of the superseding indictment. The district court sentenced Sampson to death on both counts. United States v. Sampson, 300 F.Supp.2d 275, 276 (D.Mass.2004). The district court denied Sampson's ensuing motions for judgment as a matter of law, a new penalty-phase trial, and other relief. Sampson III, 332 F.Supp.2d at 341. This appeal followed.

II. THE CONSTITUTIONAL CLAIMS

Sampson raises six types of constitutional claims. Most of them are attacks on the FDPA. First, Sampson argues that the FDPA, which authorizes prosecutors to decide whether to seek the death penalty, is unconstitutional because it does not require the aggravating factors needed for a sentence of death to be presented to a grand jury as mandated by Ring. Relatedly, he argues that the presentation of aggravating factors to the grand jury in this case was tantamount to executive and judicial redrafting of the statute in derogation of the principles of separation of powers and legislative authority. Second, Sampson argues that because the federal death penalty is so rarely sought or imposed, the FDPA operates in a fundamentally arbitrary and capricious manner (and, thus, is invalid as violative of the Eighth Amendment). Third, he argues that the absence of a principled basis for distinguishing between cases in which the federal death penalty is imposed and those in which it is not renders the FDPA unconstitutional. Fourth, he argues that the federal death penalty is sought on the invidious basis of race and the irrational basis of geography (and, thus, is unconstitutional). Fifth, he argues that continued enforcement of the federal death penalty will lead to execution of a significant number of innocent persons and that, therefore, the FDPA and the death penalty itself are unconstitutional. Finally, he argues that the death penalty is per se unconstitutional. Sampson supports his arguments with Brandeis-brief type information from studies about the operation in fact of the FDPA.

The district court rejected each of these claims after careful analysis. See Sampson II, 275 F.Supp.2d at 62-66, 71-94; Sampson I, 245 F.Supp.2d at 330-38. Concluding, as we do, that nearly all of the claims are foreclosed by Supreme Court precedent, we echo this holding.

Before addressing the issues, we confirm some basic principles applicable to judicial review. A district court's rulings on questions of law, including constitutional questions, engender de novo review. See United States v. Bender, 221 F.3d 265, 268 (1st Cir.2000); see also United States v. Marenghi, 109 F.3d 28, 31 (1st Cir. 1997). Statutes duly enacted by Congress are presumed to be constitutional. INS v. Chadha, 462 U.S. 919, 944, 103 S.Ct. 2764, 77 L.Ed.2d 317 (1983). Thus, the burden of proving that the FDPA is unconstitutional is on the challenger (here, Sampson). Lujan v. G & G Fire Sprinklers, Inc., 532 U.S. 189, 198, 121 S.Ct. 1446, 149 L.Ed.2d 391 (2001). Last ? but surely not least ? when the Supreme Court has directly decided an issue, we must "follow the case [that] directly controls, leaving to [the Supreme] Court the prerogative of overruling its own decisions." Rodriguez de Quijas v. Shearson/Am. Express, Inc., 490 U.S. 477, 484, 109 S.Ct. 1917, 104 L.Ed.2d 526 (1989). With these principles in mind, we turn to Sampson's constitutional claims.

A. Ring-Related Claims.

We begin with Sampson's multi-faceted claim that the FDPA is unconstitutional under Ring. Sampson argues that the FDPA "suffers from a fatal flaw," Appellant's Br. at 199, in that it provides for the prosecutor, not a grand jury, to set out by allegation the aggravating factors necessary for a sentence of death whereas the Constitution, as interpreted by the Ring Court, requires that these factors be presented to a grand jury and charged in an indictment. He further argues that allowing the prosecutor to select the aggravating factors and present them to the grand jury in his case constituted "improper executive and judicial redrafting of the statute." Id. We do not agree.

The FDPA defines the circumstances under which defendants who commit certain federal crimes may be eligible for the death penalty. A defendant who commits a qualifying offense is death-penalty eligible only if a jury finds beyond a reasonable doubt that the defendant acted with the statutorily required intent, see 18 U.S.C. §§ 3591(a)(2), 3593(b), and that at least one statutorily defined aggravating factor exists, see id. §§ 3592, 3593(c)-(e). It is only after these threshold findings are made that a jury, considering both mitigating and aggravating factors, may determine that the death penalty is appropriate. See id. § 3593(c)-(e).

Part of the statute, section 3593(a), authorizes the Department of Justice (DOJ) to determine whether to seek the death penalty in a particular case. If the government elects to seek the death penalty, the statute requires it to give the defendant notice of its election and of the aggravating factors that it plans to prove. Id. § 3593(a).

The FDPA makes no mention of the grand jury. This omission is understandable. Congress enacted the FDPA in 1994 against the backdrop of Walton v. Arizona, 497 U.S. 639, 110 S.Ct. 3047, 111 L.Ed.2d 511 (1990), in which the Supreme Court held that "the Sixth Amendment does not require that the specific findings authorizing the imposition of the sentence of death be made by the jury." Id. at 648, 110 S.Ct. 3047 (quoting Hildwin v. Florida, 490 U.S. 638, 640-41, 109 S.Ct. 2055, 104 L.Ed.2d 728 (1989) (per curiam)) (internal quotation marks omitted). Essentially, the Walton Court held that the facts necessary to render a defendant eligible for the death penalty were not elements of the offense itself, making inapplicable the Fifth Amendment requirement that the elements of an offense be charged by a grand jury in an indictment. See id. at 649, 110 S.Ct. 3047.

The Supreme Court first cast doubt on Walton in Jones v. United States, 526 U.S. 227, 119 S.Ct. 1215, 143 L.Ed.2d 311 (1999). There, the Court considered 18 U.S.C. § 2119, the carjacking statute involved in this case, and held that the statute created three separate offenses. See Jones, 526 U.S. at 251-52, 119 S.Ct. 1215. It further held that the fact that a defendant caused serious bodily injury to another during the commission of a crime was an element of a greater offense that had to be both charged in an indictment and found by a jury at trial beyond a reasonable doubt. See id. at 232-39, 252, 119 S.Ct. 1215. In reaching these conclusions, the Jones Court distinguished the sentencing factors upheld in Walton. See id. at 251, 119 S.Ct. 1215.

The next Term, the Court held that any fact that increases the maximum authorized statutory sentence "is the functional equivalent of an element of a greater offense," which must be charged in an indictment and proved beyond a reasonable doubt. Apprendi v. New Jersey, 530 U.S. 466, 490, 494 n. 19, 120 S.Ct. 2348, 147 L.Ed.2d 435 (2000).

Finally, in 2002 the Court explicitly overruled Walton. See Ring, 536 U.S. at 609, 122 S.Ct. 2428. In the wake of Ring, Supreme Court precedent now firmly establishes that the mental culpability and aggravating factors required by the FDPA must ? in addition to being included in the government's notice to seek the death penalty ? be presented to a grand jury, charged in the indictment, and proved beyond a reasonable doubt. But as we shall explain, even though this eliminates a background assumption against which the FDPA was framed, it does not render the statute unconstitutional.

Sampson contends both that there is a conflict between the FDPA and Ring, and that curing the problem would require the rewriting of the statute, which is a legislative function. This contention is unpersuasive. The courts that have considered this thesis uniformly have rejected it. See United States v. Brown, 441 F.3d 1330, 1367 (11th Cir.2006), cert. denied, ___ U.S. ___, 127 S.Ct. 1149, ___ L.Ed.2d ___ (2007); United States v. Allen, 406 F.3d 940, 949 (8th Cir.2005), cert. denied, ___ U.S. ___, 127 S.Ct. 826, 166 L.Ed.2d 665 (2006); United States v. Barnette, 390 F.3d 775, 788-90 (4th Cir.2004), vacated on other grounds, ___ U.S. ___, 126 S.Ct. 92, 163 L.Ed.2d 32 (2005); United States v. Robinson, 367 F.3d 278, 290 (5th Cir.2004); cf. United States v. Collazo-Aponte, 281 F.3d 320, 324-25 (1st Cir.2002) (rejecting a facial challenge to 21 U.S.C. § 841 because "there is nothing in the statutory language that explicitly defies Apprendi").

We agree with this line of cases; there is no irredeemable conflict between the FDPA and Ring. The FDPA does not, as Sampson suggests, grant to prosecutors exclusive authority for determining the likely existence of aggravating factors. No provision of the FDPA prohibits a grand jury from considering those factors necessary for imposition of a death sentence. The statute simply is silent with respect to the function of the grand jury. It thus is not rendered facially unconstitutional by Ring.

Sampson also presents a variation on this theme, arguing that the application of Ring to the FDPA requires impermissible judicial or executive redrafting of the statute. We think not.

What is involved in the application of Ring is a matter of procedure, not of substantive definition regarding death-penalty eligibility. After all, in the habeas context, Apprendi and Ring regularly have been held to announce a new rule of criminal procedure, not a new rule of substantive law. See United States v. Brown, 305 F.3d 304, 308-09 (5th Cir.2002); Cannon v. Mullin, 297 F.3d 989, 994 (10th Cir.2002); United States v. Warden, 286 F.3d 1059, 1063 (8th Cir.2002); United States v. Sanchez-Cervantes, 282 F.3d 664, 668 (9th Cir. 2002); McCoy v. United States, 266 F.3d 1245, 1257 n. 16 (11th Cir.2001); see also Sepulveda v. United States, 330 F.3d 55, 59 (1st Cir.2003) (treating Apprendi as having announced a rule of criminal procedure); United States v. McAllister, 272 F.3d 228, 232 (4th Cir.2001) (holding, in the context of a constitutional challenge to 21 U.S.C. § 841, that Apprendi announced a procedural rule). To cinch matters, the Jones Court made pellucid that "[t]he constitutional guarantees that g[a]ve rise to [its] concern in no way restrict the ability of legislatures to identify the conduct they wish to characterize as criminal or to define the facts whose proof is essential to the establishment of criminal liability." 526 U.S. at 243 n. 6, 119 S.Ct. 1215.

It follows, then, that the rule against massive judicial rewriting of statutes simply is not implicated here. Adhering to a court-crafted rule of criminal procedure when applying the FDPA does not constitute impermissible statutory redrafting.

In this respect, the instant case is unlike United States v. Jackson, 390 U.S. 570, 88 S.Ct. 1209, 20 L.Ed.2d 138 (1968), on which Sampson relies.1 In Jackson, the Supreme Court invalidated the death penalty provision of the Federal Kidnaping Act, which permitted only a jury to impose a death sentence. Id. at 591, 88 S.Ct. 1209. The objection was that it infringed on the right to a jury trial by encouraging a defendant to plead guilty or to waive that right in order to avoid the possibility of a death sentence. Id. at 572-73, 88 S.Ct. 1209. The government encouraged the Supreme Court to save the statute by reading it to allow a judge ? in the event of a guilty plea or bench trial ? to convene a "special jury" to determine whether the death penalty was warranted. Id. The Court rejected this suggestion, stating that it could not "create from whole cloth a complex and completely novel procedure and . . . thrust it upon unwilling defendants for the sole purpose of rescuing a statute from a charge of unconstitutionality." Id. at 580, 88 S.Ct. 1209.

This case, however, does not require us to "create from whole cloth a complex and completely novel procedure." As the district court perspicaciously noted, see Sampson I, 245 F.Supp.2d at 337, the role of the grand jury in charging the elements of an offense has long been established. See, e.g., Hamling v. United States, 418 U.S. 87, 117-18, 94 S.Ct. 2887, 41 L.Ed.2d 590 (1974) (ruling on a challenge to the sufficiency of an indictment); Russell v. United States, 369 U.S. 749, 763-64, 82 S.Ct. 1038, 8 L.Ed.2d 240 (1962) (same). Here, the government honored that role; it simply presented the grand jury with evidence of possible aggravating factors.

This case also is unlike Blount v. Rizzi, 400 U.S. 410, 91 S.Ct. 423, 27 L.Ed.2d 498 (1971), and United States v. Booker, 543 U.S. 220, 125 S.Ct. 738, 160 L.Ed.2d 621 (2005), on which Sampson further relies. In Blount, the Supreme Court invalidated two provisions of the Postal Reorganization Act because they did not conform to the constitutional requirements of an administrative censorship scheme. 400 U.S. at 421-22, 91 S.Ct. 423. The Court rejected a proposed severing construction of the statute that itself failed to comply with the Constitution and then noted that "it [was] for Congress, not [the] Court, to rewrite the statute." Id. at 419, 91 S.Ct. 423. In Booker, the Court refused to graft onto the federal sentencing guidelines a set of procedures for presenting to a jury facts necessary for sentence enhancements. 543 U.S. at 246, 125 S.Ct. 738. Instead, the Court severed from the guidelines the provision making mandatory the effect of sentencing factors not found by a jury. Id. at 245, 125 S.Ct. 738. To do otherwise, it held, "would [have] so transform[ed] the scheme that Congress created that Congress likely would not have intended the Act as so modified to stand." Id. at 249, 125 S.Ct. 738.

The statutes in question in Blount and Booker, like the statute in Jackson, were incompatible with constitutional requirements. See id. at 227-29, 125 S.Ct. 738; Blount, 400 U.S. at 417, 91 S.Ct. 423. Saving either statute, as proposed by the government, while at the same time complying with constitutional mandates, would have required the Court to perform a complete statutory rewrite, which is a legislative and not a judicial function. In contrast, allowing a grand jury to consider and charge aggravating factors under the FDPA does not have any effect either on the substantive aspects of the statute or on the discrete roles that the statute assigns to the judge, the prosecutor, and the jury, respectively.

To sum up, Ring does not render the FDPA unconstitutional either on its face or as applied in this case.2

B. Arbitrary Operation.

Sampson makes two arguments in support of his claim that the FDPA is unconstitutional because it is arbitrary in its operation. First, he argues that because the federal death penalty is infrequently sought and even more infrequently carried out, its imposition is arbitrary, capricious, and therefore unconstitutional. Sampson centers this argument around Furman v. Georgia, 408 U.S. 238, 92 S.Ct. 2726, 33 L.Ed.2d 346 (1972), in which the Supreme Court struck down as unconstitutional the Georgia capital punishment statute then in effect. In a concurring opinion, Justice Stewart stated that the death sentences at issue were

cruel and unusual in the same way that being struck by lightning is cruel and unusual. For, of all the people convicted of rapes and murders in 1967 and 1968, many just as reprehensible as [those committed by petitioners], the petitioners are among a capriciously selected random handful upon whom the sentence of death has in fact been imposed.

Id. at 309-10, 92 S.Ct. 2726 (Stewart, J., concurring) (footnote omitted). Sampson argues that Justice Stewart's statement constitutes the essence of Furman. See Appellant's Br. at 238 (characterizing Furman as viewing "arbitrariness and caprice . . . as the inevitable side-effects of a rarely-imposed punishment of death"). Given this reading, he argues that because the federal death penalty is rarely sought or imposed, the FDPA is no different from the Georgia statute invalidated in Furman.

This argument mistakes the nature of the arbitrariness concern in the Supreme Court's jurisprudence. In the thirty-four years since Furman was decided, the Court has made clear that its decision was not based on the frequency with which the death penalty was sought or imposed. Rather, the primary emphasis of the Court's death penalty jurisprudence has been the requirement that the discretion exercised by juries be guided so as to limit the potential for arbitrariness. Thus, in Gregg v. Georgia, 428 U.S. 153, 96 S.Ct. 2909, 49 L.Ed.2d 859 (1976), the Court, upholding the revised Georgia capital sentencing statute, described Furman as "mandat[ing] that where discretion is afforded a sentencing body on a matter so grave as the determination of whether a human life should be taken or spared, that discretion must be suitably directed and limited so as to minimize the risk of wholly arbitrary and capricious action." Id. at 189, 96 S.Ct. 2909 (opinion of Stewart, Powell, and Stevens, JJ.).

Together, Furman and Gregg require that a death penalty statute "(1) rationally narrow the class of death-eligible defendants[ ] and (2) permit a jury to render a reasoned, individualized sentencing determination based on a death-eligible defendant's record, personal characteristics, and the circumstances of his crime." Kansas v. Marsh, ___ U.S. ___, 126 S.Ct. 2516, 2524-25, 165 L.Ed.2d 429 (2006). As the Supreme Court recognized in a different context, these requirements "further an essential need of the Anglo-American criminal justice system ? to balance the desirability of a high degree of uniformity against the necessity for the exercise of discretion." McCleskey v. Kemp, 481 U.S. 279, 312 n. 35, 107 S.Ct. 1756, 95 L.Ed.2d 262 (1987). Like the statute upheld in Gregg, the FDPA fully meets the requirements of guided discretion, suitably directing and limiting the leeway afforded to the decisionmakers.

Nor does the frequency with which the federal death penalty is sought render the FDPA unconstitutional. To the extent that there may be an independent constitutional concern as to the decisional process by which the government decides if it will seek the death penalty, that process contains numerous safeguards built into an articulated death penalty protocol. See United States Attorneys' Manual § 9-10.000, http://www.usdoj.gov/usao/eousa/foia ? reading ? room/usam/title9/10m crm. htm.3 The process, therefore, is not arbitrary. See Gregg, 428 U.S. at 195, 96 S.Ct. 2909.

Sampson's second argument is that the FDPA is unconstitutional because there is no principled basis for distinguishing between those cases in which the federal death penalty is imposed and those in which it is not. His argument is premised on Eddings v. Oklahoma, 455 U.S. 104, 102 S.Ct. 869, 71 L.Ed.2d 1 (1982), in which the Supreme Court stated that "capital punishment [must] be imposed fairly, and with reasonable consistency, or not at all." Id. at 112, 102 S.Ct. 869. This argument ignores the remainder of the Eddings Court's discussion of consistency, in which the Court recognized that "a consistency produced by ignoring individual differences is a false consistency." Id. Indeed, the thrust of Eddings is that those who make sentencing decisions must be permitted to focus on the individual characteristics of the defendant and the circumstances of the crime. Id. And, finally, the argument cannot survive McCleskey, in which the Court stated that "[t]he Constitution is not offended by inconsistency in results based on the objective circumstances of the crime. Numerous legitimate factors may influence . . . a defendant's ultimate sentence, even though they may be irrelevant to his actual guilt." 481 U.S. at 307 n. 28, 107 S.Ct. 1756.

In all events, the "evidence" that Sampson submits is wholly inadequate to prove that the death penalty has been imposed in an arbitrary manner. The summaries on which Sampson relies to demonstrate inconsistency are devoid of details and fail to account for the objective circumstances of the underlying crimes. Even the more detailed verdict sheets that he submitted to the district court fail to establish arbitrary imposition of the death penalty. On this record and mindful of the teachings of McCleskey, we decline Sampson's invitation to ignore individual differences across offenders and offenses. Consequently, there is no principled basis for finding that similar cases are treated differently.

C. Other Challenges to the FDPA.

Sampson's remaining challenges to the constitutionality of the FDPA are those related to race, geography, and innocence. Sampson (who is white) raises no argument that he was sentenced to death because of his race, the race of his victims, or the geographic location in which he was sentenced. Nor does he claim to be actually innocent.

What, then, is his claim? In essence, Sampson attempts to assert the rights of other capital defendants. His claim is that, although he himself was not disadvantaged by race or geography and although he is not innocent, the FDPA is unconstitutional because it has these untoward effects elsewhere. And if the FDPA is unconstitutional, his thesis runs, he may not be sentenced under it.

It is questionable whether Sampson has standing to challenge the constitutionality of the federal death penalty on these grounds. See County Court v. Allen, 442 U.S. 140, 155, 99 S.Ct. 2213, 60 L.Ed.2d 777 (1979) ("As a general rule, if there is no constitutional defect in the application of the statute to a litigant, he does not have standing to argue that it would be unconstitutional if applied to third parties in hypothetical situations."); see also Broadrick v. Oklahoma, 413 U.S. 601, 610, 93 S.Ct. 2908, 37 L.Ed.2d 830 (1973) (citing cases).

Because there is no Supreme Court precedent directly on point and because "death is . . . different," Gardner v. Florida, 430 U.S. 349, 357, 97 S.Ct. 1197, 51 L.Ed.2d 393 (1977), we will assume arguendo that Sampson has standing to pursue these arguments. He nonetheless fails to prove the unconstitutionality of the FDPA.

1. Race-and-Geography-Related Claims. We take first Sampson's claims that the FDPA is unconstitutional because the death penalty is sought based on the race of the defendant and victim and on the locale in which the defendant is charged. Sampson's race-based claims implicate the Fifth and Eighth Amendments. His geography-related claim implicates the Eighth Amendment.4

Sampson's challenges are based primarily on a 2000 DOJ study of the administration of the federal death penalty from 1988 to 2000, and on a 2001 supplemental report. He reads the studies as demonstrating a pattern of discrimination against minority defendants and against defendants in the South. For example, he notes that over 70% of federal defendants for whom the death penalty was sought were non-whites. Similarly, between 1995 and 2000, only slightly more than half of the districts in the federal system submitted a case to the Attorney General with a recommendation for capital prosecution. Sampson also cites evidence of a white-victim effect, including one study showing that the death penalty authorization rate is 37% in white-victim cases, but only 21% in minority-victim cases.

Bare statistical discrepancies are insufficient to prove a Fifth Amendment violation with respect to the implementation of a statute. This principle is firmly established by McCleskey. 481 U.S. at 292, 107 S.Ct. 1756 (stating that "to prevail under the Equal Protection Clause, [a defendant] must prove that the decisionmakers in his case acted with discriminatory purpose").5 It applies here: because Sampson has presented no specific evidence of purposeful discrimination either against himself or against those southern and minority defendants upon whom he purports to base his claim, his Fifth Amendment challenge fails.

By like token, Sampson's Eighth Amendment claims cannot succeed. The McCleskey Court, in rejecting an Eighth Amendment claim based on a statistical study indicating race-based discrepancies in capital sentencing, stated:

Apparent disparities in sentencing are an inevitable part of our criminal justice system. . . . [O]ur consistent rule has been that constitutional guarantees are met when "the mode [for determining guilt or punishment] itself has been surrounded with safeguards to make it as fair as possible." Where the discretion that is fundamental to our criminal process is involved, we decline to assume that what is unexplained is invidious.

481 U.S. at 312-13, 107 S.Ct. 1756 (second alteration in original) (citation omitted) (quoting Singer v. United States, 380 U.S. 24, 35, 85 S.Ct. 783, 13 L.Ed.2d 630 (1965)). The statistics submitted by Sampson are no more probative than those rejected in McCleskey. The DOJ study provides no basis for attributing the statistical discrepancies with respect to geography and race in FDPA prosecutions to discrimination rather than to other factors, such as differences in the nature of the crimes involved. McCleskey prohibits us from assuming that "what is unexplained is invidious." Id.

2. Innocence-Related Claims. Sampson's final claims regarding the FDPA's constitutionality concern the risk of executing innocent defendants. Again, we assume arguendo that Sampson, who has admitted his guilt by pleading to the charges against him, has standing to assert the interests of the innocent.

Sampson appears to make two closely related Fifth Amendment arguments, both of which derive from his reliance on United States v. Quinones, 205 F.Supp.2d 256 (S.D.N.Y.), rev'd, 313 F.3d 49 (2d Cir. 2002).6 Sampson's first argument is that because factual studies establish that innocent defendants have been convicted and sentenced to death, the Fifth Amendment right to procedural due process demands that defendants be permitted to attempt to prove their innocence throughout their natural lives. His second argument is that the risk of executing the innocent offends Fifth Amendment substantive due process protections.

As with Sampson's other constitutional challenges to the FDPA, these arguments are foreclosed by Supreme Court precedent. For years, a perennial debate has raged over the propriety of capital punishment in view of the omnipresent risk of executing innocent defendants. See Quinones, 313 F.3d at 63-64. Withal, the Court has declined, for over two centuries, to hold the death penalty unconstitutional per se. In Furman, for example, both Justices Marshall and Brennan explicitly recognized that the risk of executing the innocent is inherent in capital punishment. See 408 U.S. at 364, 366-68, 92 S.Ct. 2726 (Marshall, J., concurring); id. at 290, 92 S.Ct. 2726 (Brennan, J., concurring). Despite this stark reality, no majority of Justices ever has held the death penalty unconstitutional on those grounds.

The Court squarely addressed the issue of the risk of executing the innocent in Herrera v. Collins, 506 U.S. 390, 113 S.Ct. 853, 122 L.Ed.2d 203 (1993). It affirmed the denial of a petition for a writ of habeas corpus notwithstanding a claim by the petitioner that new evidence could prove his actual innocence. Id. at 393, 113 S.Ct. 853. The Court noted that "[c]laims of actual innocence based on newly discovered evidence have never been held to state a ground for federal habeas relief absent an independent constitutional violation occurring in the underlying state criminal proceeding." Id. at 400, 113 S.Ct. 853. The Court continued:

We may assume, for the sake of argument in deciding this case, that in a capital case a truly persuasive demonstration of "actual innocence" made after trial would render the execution of a defendant unconstitutional, and warrant federal habeas relief if there were no state avenue open to process such a claim. But . . . the threshold showing for such an assumed right would necessarily be extraordinarily high.

Id. at 417, 113 S.Ct. 853. We understand Herrera to leave open the possibility that, in a particular instance of newly discovered, highly persuasive evidence of innocence, emerging at a time when no state remedy remains available, a federal court might be able to issue a writ of habeas corpus under the Constitution to prohibit execution. That is a far cry, however, from saying that the FDPA is unconstitutional.

Indeed, Herrera supports the constitutionality of the statute. Despite the "unalterable fact that our judicial system, like the human beings who administer it, is fallible," id. at 415, 113 S.Ct. 853, the Herrera Court could not say that the "refusal to entertain petitioner's newly discovered evidence eight years after his conviction" transgressed his due process rights. Id. at 411, 113 S.Ct. 853.

This is entirely consistent with the Court's opinion in Chapman v. United States, 500 U.S. 453, 111 S.Ct. 1919, 114 L.Ed.2d 524 (1991), which prevents inferior federal courts from holding capital punishment per se violative of due process. See id. at 465, 111 S.Ct. 1919. The Chapman Court held that under the Due Process Clause,

[e]very person has a fundamental right to liberty in the sense that the Government may not punish him unless and until it proves his guilt beyond a reasonable doubt at a criminal trial conducted in accordance with the relevant constitutional guarantees. But a person who has been so convicted is eligible for, and the court may impose, whatever punishment is authorized by statute for his offense, so long as that penalty is not cruel and unusual, and so long as the penalty is not based on an arbitrary distinction that would violate the Due Process Clause of the Fifth Amendment.

Id. (citations omitted); see United States v. Inglesi, 988 F.2d 500, 503 (4th Cir.1993) (quoting Chapman for the proposition that "the relevant due process inquiry on [a constitutional challenge in the sentencing context] is only whether the sentence at issue is `based on an arbitrary distinction,' or, instead, on `a rational sentencing scheme'"). The Supreme Court has held that capital punishment is not per se cruel and unusual, see Gregg, 428 U.S. at 187, 96 S.Ct. 2909 (opinion of Stewart, Powell, and Stevens, JJ.); id. at 226, 96 S.Ct. 2909 (opinion of White, J., joined by Burger, C.J., and Rehnquist, J.), and there is no allegation here that the execution of innocent individuals results from arbitrary distinctions or application of the FDPA.

We are bound by this Supreme Court precedent. Accordingly, we join those courts of appeals that have rebuffed similar arguments, see Robinson, 367 F.3d at 290; Quinones, 313 F.3d at 61-69, and reject Sampson's claims that the federal death penalty is unconstitutional because it necessarily entails a risk of executing the innocent.

D. The Death Penalty Simpliciter.

In a final catchall argument, Sampson asks us to declare the death penalty unconstitutional as cruel and unusual punishment and a per se denial of due process in all cases. Sampson concedes that under Supreme Court precedent the argument fails. Yet, he urges this court to rule to the contrary because the death penalty is "racist to its very core," Appellant's Br. at 291; leads to the execution of innocent people; and vests an unacceptable level of unreviewable discretion in prosecutors. He adds, moreover, his belief that the American public eventually will determine that capital punishment is wrong and immoral.

In Gregg, the Supreme Court held that "the death penalty is not a form of punishment that may never be imposed, regardless of the circumstances of the offense, regardless of the character of the offender, and regardless of the procedure followed in reaching the decision to impose it." 428 U.S. at 187, 96 S.Ct. 2909 (opinion of Stewart, Powell, and Stevens, JJ.); see id. at 226, 96 S.Ct. 2909 (opinion of White, J., joined by Burger, C.J., and Rehnquist, J.); accord Roberts v. Louisiana, 428 U.S. 325, 331, 96 S.Ct. 3001, 49 L.Ed.2d 974 (1976) (opinion of Stewart, Powell, and Stevens, JJ.); id. at 350-56, 96 S.Ct. 3001 (White, J., joined by Burger, C.J., Blackmun, J. and Rehnquist, J., dissenting). The Chapman Court laid out the test, under which Sampson cannot prevail, for determining whether a particular form of punishment violates due process. Because Gregg, Roberts, and Chapman are binding upon us, we reject Sampson's bedrock claim and hold that the death penalty itself is not unconstitutional.

III. CLAIMS OF TRIAL ERROR

We turn next to Sampson's manifold claims of trial error. We begin by evaluating alleged errors in the charge and the jury selection process. We then proceed to Sampson's evidence-related claims, including challenges to several of the district court's rulings and to evidentiary sufficiency. We conclude by addressing a potpourri of other claims, including Sampson's invocation of the cumulative error doctrine.

A. Jury Instructions.

We begin with the district court's charge to the jury. Sampson alleges three strains of instructional error. Because each of them presents a properly preserved question of law, we afford de novo review, taking into account the charge as a whole and the body of evidence presented at trial. See United States v. Woodward, 149 F.3d 46, 68-69 (1st Cir.1998); United States v. Alzanki, 54 F.3d 994, 1001 (1st Cir.1995).

1. Weighing. Sampson's primary complaint of instructional error relates to the district court's charge on the weighing of aggravating and mitigating factors. In Sampson's view, these instructions violated the FDPA and, in the bargain, infringed upon constitutional protections. Specifically, he argues that the instructions (i) erroneously invited jurors to apply their own idiosyncratic standards to the weighing process and (ii) failed to require that they find beyond a reasonable doubt that aggravating factors outweighed mitigating factors before voting to impose the death penalty.

Because our assessment of Sampson's plaints must take into account the weighing instructions as a whole, Woodward, 149 F.3d at 69, we reprint the pertinent portions here:

[Y]ou are called upon to decide if the proven aggravating factors or factor sufficiently outweigh the proven mitigating factors. This is not a matter of arithmetic. You're not being asked to simply count the total number of aggravating and mitigating factors and reach a decision based on which number is greater. Instead, you must consider the weight and value that you feel should be given to each factor.

Different factors may be given different weights or values by different jurors. You might find that a single aggravating factor is serious enough to outweigh several mitigating factors. Similarly, a single mitigating factor might outweigh several aggravating factors.

If you find that the government has not proven that the aggravating factor or factors outweigh the mitigating factors at all, you may not vote to impose the death penalty on the count that you're considering. If, however, you decide that the prosecution has proven that the aggravating factor or factors outweigh the mitigating factors, you must decide if the prosecution has also proven beyond a reasonable doubt that those aggravating factors sufficiently outweigh the mitigating factors to make death the appropriate penalty for Mr. Sampson's crime rather than life in prison without possibility of release.

The law does not define what is sufficient to make death the appropriate penalty. Here, the law relies on each of you as a representative of our community to consult your conscience and determine what is sufficient to justify Mr. Sampson's execution. Thus, your decision as to what the appropriate sentence is will depend in part on what is sufficient for you. If you find that the government has proven that the aggravating factors slightly outweigh the mitigating factors and that is sufficient for you to find that death is the appropriate penalty, you may properly vote for death.

On the other hand, even if the government has proven to you that the aggravating factors greatly outweigh the mitigating factors, you may properly decide that this is not sufficient to justify a sentence of death because, for you, even more is required for you to find that a man should die.

However you personally define sufficiency, the prosecution must convince you beyond a reasonable doubt that the aggravating factor or factors sufficiently outweigh the mitigating factors to make death the appropriate penalty in this case.

As I told you earlier, this is a heavy burden. More than a strong probability is required. You must be certain beyond any reasonable doubt that a death sentence should be imposed before voting for it.

Death is, of course, the ultimate irreversible punishment. You must not sentence Gary Sampson to die unless you are convinced beyond a reasonable doubt that death is the appropriate punishment.

As I've told you previously, the law never requires that any or all of you find that the death penalty is justified. Any one of you may decline to impose a death sentence. If you decide that the prosecution has not proven beyond a reasonable doubt that the death penalty is justified, you do not have to give a reason for that decision. The law does require that you follow the process that I've explained and then make a reasoned moral judgment.

Sampson argues initially that the sufficiency language embedded in this part of the charge violates both the FDPA and the Eighth Amendment. He asserts that, by inviting each juror to use his or her own definition of sufficiency, the district court "offered its own idiosyncratic definition of the language of the statute," Appellant's Br. at 62-63, and failed to provide adequate sentencing guidance as required by the Eighth Amendment in capital cases.

To determine whether the sufficiency language comported with the FDPA, we start by consulting the statute's text; we then proceed, if necessary, to examine its structure and surrounding provisions. See Green, 407 F.3d at 441-43.

The relevant section of the FDPA, 18 U.S.C. § 3593(e), which we set out in the margin,7 provides no definition of the phrase "sufficiently outweigh." Thus, the court's definition of sufficiency does not explicitly contradict the statutory text. At any rate, the court's definition is fully consistent with the immediately preceding paragraph, which provides that "any member of the jury who finds the existence of a mitigating factor may consider such factor established." Id. § 3593(d). For jurors to consider different mitigating factors, they would necessarily need to engage in the type of individualized weighing described by the district court. Given the statutory phrase "sufficiently outweigh," Sampson's attack under the FDPA fails.

We hold, as well, that the sufficiency instruction does not violate the Eighth Amendment. Sampson argues strenuously that the Eighth Amendment, if not the statute, requires that the jury be instructed to follow a uniform method of weighing, precluding individual approaches. We disagree.

The Supreme Court repeatedly has emphasized that key to harmonizing a capital sentencing scheme with the proscription against cruel and unusual punishment is an individualized determination by the jury of whether, taking into account all the relevant aggravating and mitigating factors, a death sentence is appropriate in a particular case. See, e.g., Tuilaepa v. California, 512 U.S. 967, 973, 114 S.Ct. 2630, 129 L.Ed.2d 750 (1994); Zant v. Stephens, 462 U.S. 862, 879, 103 S.Ct. 2733, 77 L.Ed.2d 235 (1983). Sampson correctly points out that the jury's discretion in sentencing must be "suitably directed and limited so as to minimize the risk of wholly arbitrary and capricious action." Gregg, 428 U.S. at 189, 96 S.Ct. 2909 (opinion of Stewart, Powell, and Stevens, JJ.). However, once a jury has found a defendant death-eligible, it may be given unfettered discretion in the weighing process. See Tuilaepa, 512 U.S. at 979, 114 S.Ct. 2630 (explaining that "[a] capital sentencer need not be instructed how to weigh any particular fact in the capital sentencing decision"); see also Ayers v. Belmontes, ___ U.S. ___, 127 S.Ct. 469, 479, 166 L.Ed.2d 334 (2006). Sampson's argument that the jury needed more guidance in order to weigh aggravators against mitigators is foreclosed by these precedents.

Sampson also alleges that the weighing instructions failed to require jurors to find beyond a reasonable doubt that aggravating factors outweighed mitigating factors, and thus violated the FDPA and the Fifth and Sixth Amendments. We can readily dismiss the statutory argument. The FDPA makes no mention of the reasonable doubt standard in the context of weighing aggravating and mitigating factors, see 18 U.S.C. § 3593(e), but it does reference the reasonable doubt standard in two proximate sections, see id. §§ 3591(a)(2), 3593(c). Because the inclusion of a term in one part of a statute is persuasive evidence that its omission elsewhere is deliberate, see Green, 407 F.3d at 443, we hold that Congress did not intend the reasonable doubt standard to apply to the weighing process. That being so, Sampson cannot have been harmed by the instruction given.

Sampson's constitutional arguments on this front are no more persuasive. Relying on a procession of Supreme Court cases, see, e.g., Booker, 543 U.S. at 244, 125 S.Ct. 738; Blakely v. Washington, 542 U.S. 296, 305, 124 S.Ct. 2531, 159 L.Ed.2d 403 (2004); Ring, 536 U.S. at 609, 122 S.Ct. 2428; Apprendi, 530 U.S. at 490, 120 S.Ct. 2348, he contends that the balance between aggravating and mitigating factors is a "fact" that should have been found by the jury beyond a reasonable doubt. The district court's alleged failure to instruct that the reasonable doubt standard applied to this "fact" was, therefore, error.

Sampson's attempt to draw an analogy between this weighing determination and the sentencing determinations found unconstitutional in the Apprendi line of cases lacks force. In Blakely, for example, the Court invalidated a sentence that had been elevated above the statutory maximum based upon a finding of "deliberate cruelty" because the facts supporting that finding were found by a judge, not by the jury beyond a reasonable doubt. See 542 U.S. at 303, 124 S.Ct. 2531. The case at hand is different in kind because, under the FDPA, the jury already had found beyond a reasonable doubt the facts needed to support a sentence of death ? the presence of aggravating factors and the requisite intent ? before it reached the weighing stage. See 18 U.S.C. §§ 3591(a)(2), 3593(c)-(e).

Sampson tries to circumvent this logic by pointing out that the weighing determination itself is essential to imposing a death sentence. He repeatedly refers to Justice Scalia's statement "that all facts essential to imposition of the level of punishment that the defendant receives ? whether the statute calls them elements of the offense, sentencing factors, or Mary Jane ? must be found by the jury beyond a reasonable doubt." Ring, 536 U.S. at 610, 122 S.Ct. 2428 (Scalia J., joined by Thomas, J., concurring). This argument founders, however, because it assumes, without the slightest support, that the weighing of aggravating and mitigating factors is a fact. This assumption is incorrect. As other courts have recognized, the requisite weighing constitutes a process, not a fact to be found. See United States v. Purkey, 428 F.3d 738, 750 (8th Cir.2005) (characterizing the weighing process as "the lens through which the jury must focus the facts that it has found" to reach its individualized determination), cert. denied, ___ U.S. ___, 127 S.Ct. 433, 166 L.Ed.2d 307 (2006); see also Ford v. Strickland, 696 F.2d 804, 818 (11th Cir.1983); Gray v. Lucas, 685 F.2d 139, 140 (5th Cir.1982) (per curiam). The outcome of the weighing process is not an objective truth that is susceptible to (further) proof by either party. Hence, the weighing of aggravators and mitigators does not need to be "found." We hold, therefore, that the district court's instructions were free from Apprendi error.

Sampson has a residual argument: that the district court's simultaneous and alternating references to both a personal notion of sufficiency and a reasonable doubt standard were confusing and inconsistent. We evaluate this argument by determining whether there exists a reasonable likelihood that the jury interpreted the instructions in a way that would violate the law. See Boyde v. California, 494 U.S. 370, 380, 110 S.Ct. 1190, 108 L.Ed.2d 316 (1990); see also Jones v. United States, 527 U.S. 373, 390, 119 S.Ct. 2090, 144 L.Ed.2d 370 (1999). Under this approach, a defendant cannot rely solely on how a single hypothetical juror might have interpreted a challenged instruction. See Boyde, 494 U.S. at 380, 110 S.Ct. 1190 (noting the "strong policy against retrials . . . where the claimed error amounts to no more than speculation").8 After careful assessment of the instructions as a whole, we reject Sampson's contention that the challenged instruction is likely to have caused harmful juror confusion.

Sampson places great emphasis on the language telling jurors that they could impose the death penalty if the aggravating factors "slightly outweigh[ed]" the mitigating factors. This phrase was followed immediately, however, by an assurance that jurors could refuse to vote for a death sentence "even if the government ha[d] proven to [them] that the aggravating factors greatly outweigh[ed] the mitigating factors." The court further instructed that however jurors defined sufficiency, the prosecution had to convince them "beyond a reasonable doubt that the aggravating factor or factors sufficiently outweigh the mitigating factors to make death the appropriate penalty in [the] case." Viewed in its entirety, this instruction clearly communicated to jurors the relatively straightforward proposition that they, as individuals, had to be certain that death was the appropriate punishment before imposing it.

Even if we assume (favorably to Sampson) that the instruction might have been mildly confusing, any error was benign. In a capital case, as in any other case, a confusing instruction may be harmless. See Boyde, 494 U.S. at 383-84, 110 S.Ct. 1190. Here, we discern no reasonable likelihood that jurors may have interpreted the instruction in a way that could have harmed Sampson. There are only two possibilities: either the jurors eschewed the reasonable doubt standard vis-à-vis the weighing process (which, as we have held, would have comported fully with the law) or they applied the reasonable doubt standard (which would have benefitted Sampson by imposing a more onerous burden on the government). Any error was, therefore, patently harmless.9

2. Vulnerable Victim. The FDPA contemplates that the government must show the presence of at least one enumerated aggravating factor in order to render a defendant death-eligible. See 18 U.S.C. § 3593(e). In this case, the jury unanimously found several statutory aggravating factors: that Sampson committed both the McCloskey and Rizzo murders in an "especially heinous, cruel, or depraved manner," id. § 3592(c)(6); that McCloskey was "particularly vulnerable due to . . . infirmity," id. § 3592(c)(11); and that Rizzo was murdered "after substantial planning and premeditation," id. § 3592(c)(9). With respect to certain of these factors, Sampson objects to the lower court's jury instructions. We turn next to his challenge anent the "vulnerable victim" instructions.

The FDPA permits the vulnerability of a victim to be used as an aggravating factor and defines that quality as a showing that the victim was "particularly vulnerable due to old age, youth, or infirmity." Id. § 3592(c)(11). In this case, the government contended that Phillip McCloskey was a vulnerable victim. After finding the evidence sufficient to support a vulnerable victim instruction vis-à-vis McCloskey, the district court instructed as follows:

Question 3B asks whether it's been proven to each and every one of you beyond a reasonable doubt that Philip McCloskey was particularly vulnerable due to infirmity. In essence, the Federal Death Penalty statute provides that a defendant is especially blameworthy if he murders someone who is particularly vulnerable to being killed because he has an infirmity which made him less able to escape or resist attack than most people. In this context, to be vulnerable means to be subject to being attacked or injured because of some weakness. To be particularly vulnerable means to be especially or significantly vulnerable or to be vulnerable to a particularly high degree.

An infirmity is a physical or mental weakness or flaw. To prove this aggravating factor, it must also be proven beyond a reasonable doubt to each and every one of you that there was a connection between Mr. McCloskey's alleged vulnerability and his death. This means that any infirmity which you find made Mr. McCloskey particularly vulnerable must somehow have contributed to his death. However, the requirement of a connection between any proven infirmity and a person's death does not mean that the prosecution must prove that the defendant knew of Mr. McCloskey's alleged vulnerability and targeted him because of it. Rather, it means that the prosecution must prove that, once targeted, Mr. McCloskey was significantly more vulnerable to being killed because he had an infirmity.

Sampson alleges that this instruction violated his Eighth Amendment rights because it did not require the jury to find that he knew McCloskey was particularly vulnerable due to infirmity and targeted McCloskey on that account. To support this contention, he argues that this aggravating factor, absent an element of scienter, was based on the "mere happenstance" of the victim's infirmity, Appellant's Br. at 179, and did not adequately narrow the class of persons eligible for the death penalty. See Arave v. Creech, 507 U.S. 463, 474, 113 S.Ct. 1534, 123 L.Ed.2d 188 (1993).

Sampson's remonstrance notwithstanding, it is clear that the challenged instruction complies with the FDPA. The statutory provision describing this aggravating factor does not contain a scienter element. See 18 U.S.C. § 3592(c)(11). By contrast, other statutory aggravating factors contain explicit scienter requirements. See, e.g., id. § 3592(c)(5) (requiring a showing that "[t]he defendant . . . knowingly created a grave risk of death"); id. § 3592(d)(4) (requiring a showing that the defendant either used a firearm or "knowingly directed ... another to use a firearm"); id. § 3592(d)(8) (requiring a showing that the defendant was aware of the presence of a potentially lethal adulterant). Because "the intentional inclusion of a[n] [element] in one part of the statute persuasively indicates that the exclusion of such a[n] [element] in another part of the same statute was intentional," Green, 407 F.3d at 443, we conclude, without serious question, that Congress did not intend that application of the vulnerable victim aggravating factor would depend upon proof of scienter.

Sampson's fallback position is that any version of the vulnerable victim aggravator that omits a scienter requirement is unconstitutional. We think not.

The Supreme Court has stated that an aggravating factor must satisfy two criteria in order to comport with the Eighth Amendment. First, the statutory language must be clear and specific enough to furnish guidance to the factfinder. Arave, 507 U.S. at 470-74, 113 S.Ct. 1534. Second, the factor must provide a principled basis for distinguishing between those who deserve capital punishment and those who do not. Id. at 474, 113 S.Ct. 1534. Viewing the FDPA's vulnerable victim factor through the prism of these requirements, we agree with the Fifth Circuit's conclusion that the aggravator, even without a scienter requirement, satisfies both criteria.10 See United States v. Bourgeois, 423 F.3d 501, 510-11 (5th Cir.2005), cert. denied, ___ U.S. ___, 126 S.Ct. 2020, 164 L.Ed.2d 786 (2006).

Since vulnerability and infirmity are concepts that are easily understandable by the average juror, the plain language in which the factor is couched supplies adequate guidance to jurors and judges. Cf. Arave, 507 U.S. at 471-72, 113 S.Ct. 1534 (concluding that the words "cold-blooded" and "pitiless" contained adequate content to guide a capital jury). By the same token, the factor effectively narrows the class of persons eligible for the death penalty so that not all victims can be considered particularly vulnerable due to age or infirmity. See id. at 474, 113 S.Ct. 1534 (explaining the importance of such a lack of universality). This narrowing effect is well-illustrated in the case at hand by the fact that the government did not charge the vulnerable victim factor with respect to the Rizzo murder. In the final analysis, then, the vulnerable victim factor provides adequate guidance to the jury and effectively circumscribes the class of defendants to whom it applies. Consequently, we hold that it passes Eighth Amendment muster.

In an effort to blunt the force of this reasoning, Sampson asks us to extrapolate from another line of death penalty cases the additional requirement that an aggravating factor must directly relate to a defendant's moral culpability (and, thus, his knowledge). See Tison v. Arizona, 481 U.S. 137, 149, 107 S.Ct. 1676, 95 L.Ed.2d 127 (1987) (explaining that a criminal sentence must be "directly related to the personal culpability of the criminal offender"); Enmund v. Florida, 458 U.S. 782, 801, 102 S.Ct. 3368, 73 L.Ed.2d 1140 (1982) (stating that punishment must be must be "tailored to . . . personal responsibility and moral guilt"). On this basis, Sampson strives to convince us that the absence of a mental state requirement in the vulnerable victim factor renders it unconstitutional.

We are not persuaded. The Enmund Court invalidated, as violative of the Eighth Amendment, the death sentence of a getaway-car driver who, although participating in an armed robbery, did not intend that lethal force be used. 458 U.S. at 801, 102 S.Ct. 3368. The Court reasoned that the punishment was disproportionate to the conduct and, thus, violated the Eighth Amendment. Id. at 797-98, 102 S.Ct. 3368.

In Tison, however, the Court held that death is not a disproportionate sentence for a defendant who, while not intending to kill his victims, is a major player in the underlying felony and demonstrates a reckless indifference to human life. 481 U.S. at 157-58, 107 S.Ct. 1676. If the death penalty is not disproportionate for this type of defendant, it follows inexorably that the death penalty is not disproportionate for Sampson ? a defendant who (the jury found) intentionally murdered his victims.

In all events, neither Tison nor Enmund was concerned with the evaluation of a specific aggravating factor. The implausibility of Sampson's attempted application of these cases to an aggravating factor is underscored by the fact that the Supreme Court implicitly has approved the use of other aggravating factors not directly related to a capital defendant's mental state at the time of the crime. See, e.g., Zant, 462 U.S. at 879, 103 S.Ct. 2733 (recognizing the validity of aggravating factors such as escape from confinement and prior felony conviction). We therefore reject Sampson's claim that the vulnerable victim factor, as limned by Congress and construed by the district court, is unconstitutional.

3. Especially Heinous, Cruel, or Depraved Conduct. In addition to McCloskey's vulnerability, the jury found beyond a reasonable doubt that both the Rizzo and McCloskey murders were committed in an especially heinous, cruel, or depraved manner. See 18 U.S.C. § 3592(c)(6). With respect to this statutory aggravating factor, the district court instructed as follows:

As I told you earlier, as a matter of law, premeditated murder alone is not sufficient to make the death penalty a sentencing option. Something more is required. More specifically, one of those "something mores" with regard to murder is that a murder must be committed in an especially heinous, cruel, or depraved manner. However, a person of ordinary sensibility could fairly characterize almost every murder as heinous, cruel, or depraved, the Supreme Court has said. Therefore, something additional must be proven to make this a truly limiting factor and to assure reasonable consistency between cases. In this case, the law provides that the killing can only be especially heinous, cruel, or depraved if it involved serious physical abuse . . . . In this case, "especially" has its usual meaning of highly or unusually great. Each of the other relevant terms has a defined meaning for the purposes of the Federal Death Penalty statute. I'll now explain those meanings to you.

"Heinous" means shockingly atrocious. In this case, a killing may be found to be especially heinous only as a result of any serious physical abuse that's proven.

"Cruel" means the defendant intended to inflict a high degree of pain. In this case, a killing may be found to be especially cruel only as a result of any serious physical abuse that is proven.

"Depraved" means that the defendant relished the killing or showed indifference to the suffering of the victim. Once again, in this case, a killing may be found to be especially depraved only as a result of any serious physical abuse that is proven.

"Serious physical abuse" has a particular legal meaning for the purpose of this case. To prove that the killing . . . involved serious physical abuse, the government must prove that Mr. Sampson intended to inflict significant damage to [the deceased's] body beyond what Mr. Sampson thought was necessary to kill him. In essence, the government must prove that Mr. Sampson intended to do more than kill [the deceased]. It must prove that he also intended to abuse his body above and beyond what was necessary to kill him. Serious physical abuse can be inflicted either before or after death. The victim does not have to be alive at the time the serious physical abuse is inflicted.

Question 3A requires two steps. First, you must determine whether it has been proven beyond a reasonable doubt that the killing . . . involved serious physical abuse, as I just defined it for you. If you do not agree unanimously that this has been proven, you must answer question 3A no and proceed to question 3B. If you do agree unanimously that serious physical abuse has been proven, you must continue to the next step. In the second step, you must decide whether that serious physical abuse proves that the crime was committed in an especially heinous, an especially cruel, or especially depraved manner, as I defined those terms for you before.

You may not consider any aspect of the crime other than proven serious physical abuse in determining whether the killing was especially heinous, especially cruel, or especially depraved. However, just because an offense involves serious physical abuse does not necessarily mean that it was committed in an especially heinous, cruel, or depraved manner. Rather, you must decide whether any proven serious physical abuse rendered the killing especially heinous, especially cruel, or especially depraved.

Sampson challenges this instruction on two primary grounds. First, noting that a defendant generally is entitled to a requested instruction on his theory of the case as long as that theory is supported by the evidence and the proffered instruction correctly states the law, see United States v. Victoria-Peguero, 920 F.2d 77, 86 (1st Cir.1990), he argues that the court's words here did not adequately communicate, as he requested, that "if the jury found that Mr. Sampson quickly inflicted a series of stab wounds intending . . . to kill his victims," that behavior would not meet the "especially heinous, cruel, or depraved" criterion. Appellant's Br. at 116-17. Second, Sampson posits that the "especially heinous, cruel, or depraved" factor is unconstitutionally vague. We consider these challenges one by one.

We need not linger long over the first challenge. The old saw that a defendant is entitled to an instruction on his theory of the case is hedged in by several qualifications. One such qualification is that a court "need not give instructions in the precise form or language requested by the defendant." United States v. Beltran, 761 F.2d 1, 11 (1st Cir.1985). An instruction suffices as long as it substantially covers the essence of the defendant's request. United States v. Noone, 913 F.2d 20, 30 (1st Cir.1990); United States v. Morris, 700 F.2d 427, 433 (1st Cir.1983).

Here, assuming Sampson was entitled to his request, see infra note 11, the district court's instruction conveyed its essence. The court repeatedly emphasized that the jury had to find serious physical abuse, which the court defined as "significant damage to [the deceased's] body beyond what Mr. Sampson thought was necessary to kill him" (emphasis supplied), as a condition to finding especially heinous, cruel, or depraved behavior. The court went on to clarify that the government had to prove that Sampson intended to do more than kill; it also had to prove that he "intended to abuse [the deceased's] body above and beyond what was necessary to kill him." We believe that this instruction accommodates Sampson's theory that if he inflicted a series of stab wounds "intending . . . to kill," that alone would not establish especially heinous, cruel, or depraved behavior. Like the instruction in Noone, 913 F.2d at 31, the instruction here provided an "appropriate legal framework for jury consideration of [the defendant's] contention." Hence, the court did not err in refusing to parrot Sampson's preferred wording in its jury instructions.

Sampson's claim of unconstitutional vagueness also falters. As discussed above, an aggravating factor must provide adequate guidance to the sentencer. See Arave, 507 U.S. at 470-74, 113 S.Ct. 1534. This requirement is satisfied when the factor, as expressed, furnishes a commonsense core of meaning that a factfinder can understand. See Jones, 527 U.S. at 400, 119 S.Ct. 2090 (plurality opinion); Tuilaepa, 512 U.S. at 973, 114 S.Ct. 2630. The delineation of an aggravator is a legislative judgment, see Tuilaepa, 512 U.S. at 974, 114 S.Ct. 2630, and judicial review of such judgments is "quite deferential." Id. at 973, 114 S.Ct. 2630.

This does not mean, of course, that a reviewing court's role is reduced to that of a rubber stamp. The Supreme Court has found that factors similar to the "especially heinous, cruel, or depraved" factor can present vagueness concerns. See, e.g., Maynard v. Cartwright, 486 U.S. 356, 363-65, 108 S.Ct. 1853, 100 L.Ed.2d 372 (1988) (analyzing Oklahoma's "especially heinous, atrocious or cruel" aggravator); Godfrey v. Georgia, 446 U.S. 420, 428-29, 100 S.Ct. 1759, 64 L.Ed.2d 398 (1980) (evaluating Georgia's "outrageously or wantonly vile, horrible and inhuman" aggravator). But such concerns can be ameliorated by a narrowing construction. See Maynard, 486 U.S. at 365, 108 S.Ct. 1853; Godfrey, 446 U.S. at 429-32, 100 S.Ct. 1759. Applying this framework, we agree with other courts of appeals that have found the FDPA's "especially heinous, cruel, or depraved" factor not unconstitutionally vague when coupled with the type of limiting instruction given by the court below. See, e.g., Bourgeois, 423 F.3d at 511; United States v. Chanthadara, 230 F.3d 1237, 1262 (10th Cir.2000); United States v. Paul, 217 F.3d 989, 1001 (8th Cir.2000).

This factor avoids facial vagueness by requiring that the offense involve serious physical abuse or torture. See Maynard, 486 U.S. at 364-65, 108 S.Ct. 1853 (approving this narrowing construction). Here, moreover, the district court carefully defined each of the relevant terms ? heinous, cruel, depraved, and serious physical abuse ? in a manner that was easily understood and that afforded the jurors a commonsense core of meaning. See Walton, 497 U.S. at 653, 110 S.Ct. 3047 (deeming such an effort "constitutionally significant"). The narrowing accomplished by the statutory inclusion of the serious physical abuse component, especially when combined with the district court's thorough instructions, leaves no room to doubt the factor's constitutionality.11

Sampson cites a plethora of state court cases in which variants of the "especially heinous, cruel, or depraved" factor have been used. See, e.g., State v. Culberth, 390 So.2d 847, 851 (La.1980); Domingues v. State, 112 Nev. 683, 917 P.2d 1364, 1377-78 (1996); State v. Hunt, 115 N.J. 330, 558 A.2d 1259, 1289-90 (1989). These decisions do not dictate a result favorable to Sampson in this case. While they illustrate the application of the legal theory discussed above ? that the enhancement requires proof of more than the harm inherent in killing ? and demonstrate the individualized evaluation that is critical to the constitutional imposition of the death penalty, they tell us little else.

Relatedly, Sampson argues for the first time on appeal that, by defining each of the component terms ? heinous, cruel, and depraved ? in relation to serious physical abuse, the district court conflated the factors in a way that might have caused jury confusion. In an apparent effort to show that such an error would not be harmless, he offers a number of articles suggesting that capital jurors often erroneously believe that death is mandatory once an aggravating factor is found. Because this claim was not preserved below, we review it for plain error. See Jones, 527 U.S. at 388-89, 119 S.Ct. 2090.

The FDPA requires that the adjectives "heinous," "cruel," and "depraved" all be defined in terms of serious physical abuse or torture. See 18 U.S.C. § 3592(c)(6). The district court found torture inapposite here and instructed the jury accordingly. It proceeded to define each adjective distinctly, in easily understandable terms, in relation to serious physical abuse.

We do not see how painstakingly defining each term as dictated by the applicable statute could conceivably serve to muddle carefully crafted instructions. To cinch matters, the lower court clearly outlined the process by which the jury was to determine the appropriate sentence. Jurors are normally presumed to follow the trial court's instructions. See Jones, 527 U.S. at 394, 119 S.Ct. 2090. We discern no basis for disregarding that presumption here. Accordingly, there was no harmful error in regard to this instruction.

B. Juror Issues.

Sampson complains about the dismissal for cause of six jurors and about the district court's allegedly improvident refusal to dismiss a seventh juror mid-trial. In each instance, he claims a violation of his constitutional right to an impartial jury. We address these plaints separately.

1. Dismissals for Cause. Sampson assails the district court's dismissal of six prospective jurors who expressed reservations about imposing the death penalty. The baseline rule is that a court appropriately may excuse a juror for his views on capital punishment if those views "would prevent or substantially impair the performance of his duties as a juror in accordance with his instructions and his oath." Adams v. Texas, 448 U.S. 38, 45, 100 S.Ct. 2521, 65 L.Ed.2d 581 (1980). We normally review a trial court's for-cause dismissal of a juror for abuse of discretion. See United States v. Gonzalez-Soberal, 109 F.3d 64, 69-70 (1st Cir. 1997). This standard of review applies equally in capital cases. See Wainwright v. Witt, 469 U.S. 412, 426, 105 S.Ct. 844, 83 L.Ed.2d 841 (1985) (noting that "deference must be paid to the trial judge who sees and hears the juror"); see also Purkey, 428 F.3d at 750.

Here, the record amply supports the district court's conclusion that the six dismissed jurors would have been substantially impaired in the performance of their duties. In reaching this conclusion, we first examine the circumstances surrounding three of the six dismissals and then turn to the remaining three dismissals.

The court had prospective jurors complete questionnaires in which the jurors, among other things, self-assessed their views about the death penalty on a scale of 1 to 10 (with "1" meaning "strongly favor" and "10" meaning "strongly oppose"). Three of the six jurors whom we are considering (Jurors 19, 77, and 205) ranked himself/herself as a "9." Another section of the questionnaire asked responders to choose the statement that best represented their views; Jurors 19 and 77 selected "I am opposed to the death penalty, and I would have a difficult time voting to impose it." Juror 205 indicated even stronger opposition, stating that he "struggle[d] to imagine a situation where [he] would vote to impose it."

To be sure, even "those who firmly believe that the death penalty is unjust may nevertheless serve as jurors in capital cases." Lockhart v. McCree, 476 U.S. 162, 176, 106 S.Ct. 1758, 90 L.Ed.2d 137 (1986). But that license is not unqualified: the ability of such jurors to serve depends upon whether they are able to subrogate their own beliefs to the need to follow the court's instructions. See id. In this instance, the district court found that none of the three jurors could satisfy that criterion. We test the court's reasoning.

After the court inquired whether she automatically would vote against the death penalty, Juror 19 stated: "I can't think of what the government would prove that would make me change my opinion on the death penalty." The court then reasonably concluded, upon observing the prospective juror's demeanor when she made that assertion, that her views would substantially impair her ability to perform her duties.

Juror 77 stated during voir dire that he did not "really believe that [the death penalty was] the appropriate sentence for anybody." This declaration left the court with the "definite impression" that although Juror 77 would "earnestly try to follow the law," he would be substantially impaired in his ability to do so. That determination was within the realm of the court's discretion.

So too the court's dismissal of Juror 205 for cause. That juror stated during voir dire that he did not know whether he could perform the duties required of a juror in a capital case. He added that he would have trouble following the law if it differed from his personal views. Given his responses to the questionnaire, no more was required to justify dismissal for cause.

The other three dismissed jurors all recounted personal circumstances that led the court to decide against compelling them to serve as jurors in a capital case. Juror 119's questionnaire revealed that he was a Catholic and a lay member of the Franciscan order, and that both organizations were opposed to the death penalty. Although he stated that he would not feel obliged to vote against the death penalty on the basis of his religion, he acknowledged that voting for the death penalty would put him "in extremely hot water with the church" and that he could "get kicked out" of the Franciscan order.

Jurors 14 and 28 revealed that they had close relatives with psychological problems and uttered repeated statements indicating that they would be unable fairly to consider and weigh evidence of Sampson's mental condition. For example, Juror 14 stated that she did not know whether she could balance evidence that Sampson had a severe emotional disturbance with other facts in deciding whether to impose a death sentence, and that she was "very concerned" about her ability to put her personal concerns aside. Juror 28's questionnaire indicated that she could not find execution justified for a mentally ill person regardless of the facts. During voir dire, she reaffirmed that she did not think that she could impose the death penalty were she to conclude that Sampson suffered from a serious mental disturbance.

There is no precise formula to guide judges in juror-qualification matters. Particularly near the margins, on-the-spot judgment plays an important part in screening out those whose ability to serve may be compromised. In each of the three instances we have just chronicled, the district court determined that the juror's personal circumstances were such as to substantially impair his or her ability to serve impartially in a capital case. Each of these instances presented a judgment call. They are, therefore, paradigmatic examples of a trial court's exercise of informed discretion. In no instance do we discern an abuse of that discretion.

While Sampson points out that each of these jurors may have indicated some degree of willingness to put aside personal biases, this fragmentary evidence is insufficient to support a finding that the trial court abused its discretion. See Witt, 469 U.S. at 425-26, 105 S.Ct. 844 ("Despite . . . lack of clarity in the printed record, . . . there will be situations where the trial judge is left with the definite impression that a prospective juror would be unable to faithfully and impartially apply the law."). Given the relevant body of evidence, we decline to second-guess the district court's first-hand impressions. Accordingly, Sampson's assignment of error fails.

2. Juror Misconduct. We come now to Sampson's claim that the district court incorrectly allowed Juror 109 to remain on the panel despite an admitted interaction with a government witness during the trial. The pertinent facts are as follows.

On Friday, December 12, 2003, a government expert witness, Dr. Michael Werner, departed the courthouse after completing his testimony. As he was leaving, Juror 109 complimented him on his memory. Dr. Werner did not respond but, rather, reported the interaction to the prosecutor. The prosecutor, in turn, informed defense counsel and the district court.

When trial resumed on Monday, Sampson moved to disqualify the juror. The court held an individual voir dire, questioned the juror about the details of the interaction, and then queried the remaining jurors (individually) to determine any potential spillover effect. Satisfied that the interaction had been both brief and non-substantive and that Juror 109 remained impartial, the court denied Sampson's motion. Sampson contests this ruling, arguing that allowing the juror to remain offended his Fifth and Sixth Amendment rights to due process and an impartial jury.

Ex parte communications between a juror and a witness during trial are presumptively prejudicial, and the trial court is required to undertake an adequate inquiry to determine their potential impact. See United States v. Gastón-Brito, 64 F.3d 11, 13 (1st Cir.1995). Because the district court is "likely to have a superior `feel' for the nuances of the case," we grant it significant latitude with respect to the scope and manner of its inquiry. United States v. Paniagua-Ramos, 251 F.3d 242, 250 (1st Cir.2001). Consequently, we review both the district court's handling of such allegations and its ensuing determinations for abuse of discretion. See id. at 249.

Here, we find no indication that the court misused its discretion. The communication in question was terse, fortuitous, and devoid of substantive content. We have attached significance before to the fact that a juror's casual ex parte communication did not concern the substance of the case, see, e.g., United States v. Angiulo, 897 F.2d 1169, 1185 (1st Cir.1990), and we think it is appropriate to continue to follow that praxis.

Here, moreover, the district court's inquiry was virtually a textbook model. The court's response was swift, its questioning pointed, and its search for any inkling of prejudice thorough. After making a face-to-face assessment of the juror's sincerity and of the possibility that other jurors had been contaminated, the court concluded that the interaction was harmless. That conclusion may not have been inevitable, but it plainly was not an abuse of discretion.

C. Evidentiary Rulings.

Sampson disputes a number of evidentiary rulings. We review adequately preserved objections to rulings admitting or excluding evidence for abuse of discretion. See United States v. Gobbi, 471 F.3d 302, 311 (1st Cir.2006). If the admission or exclusion of a piece of evidence occurs as a result of an error of law, that is a per se abuse of discretion. See Rosario-Urdaz v. Rivera-Hernandez, 350 F.3d 219, 221 (1st Cir.2003); United States v. Snyder, 136 F.3d 65, 67 (1st Cir.1998).

Where evidence is challenged on the ground that the trial court has struck the wrong balance between probative value and prejudicial effect, we accord great deference to the trier's first-hand knowledge of the case and ordinarily will sustain the district court's exercise of discretion unless its judgment is plainly incorrect. United States v. Adams, 375 F.3d 108, 111 (1st Cir.2004). Only unfair prejudice enters into this decisional calculus; "[t]he fact that a piece of evidence hurts a party's chances does not mean it should automatically be excluded." Onujiogu v. United States, 817 F.2d 3, 6 (1st Cir.1987). In all instances, harmless error principles apply. And, finally, to the extent that a claim of evidentiary error has not been preserved ? that is, when no timely and pointed objection was advanced below ? our review is only for plain error. See United States v. Flemmi, 402 F.3d 79, 86 (1st Cir.2005).

With this framework in place, we turn to Sampson's specific claims of error.

1. Crime Scene/Autopsy Evidence. Sampson challenges the admission of certain crime scene and autopsy photographs and related physical evidence pertaining to the McCloskey and Rizzo murders. The first aspect of this challenge suggests that the district court misapprehended the evidentiary standard prescribed by the FDPA for sentencing hearings and that, under a correct interpretation, the evidence in question should have been excluded. This suggestion is unrewarding.

The FDPA provides that, during a penalty-phase trial, "information may be excluded if its probative value is outweighed by the danger of creating unfair prejudice, confusing the issues, or misleading the jury." 18 U.S.C. § 3593(c). This language is similar, but not identical, to the language of Federal Rule of Evidence 403.12 A direct comparison reveals two salient differences. First, Rule 403 requires that probative value be substantially outweighed by the danger of unfair prejudice before evidence may be excluded, whereas the FDPA omits this substantiality requirement and directs that exclusion may result if the scales tip, even slightly, in favor of unfair prejudice. Second, the FDPA makes no express mention of the factors of undue delay, waste of time, and cumulativeness as grounds for exclusion.

The district court enunciated these differences in passing upon the challenged evidence. Seizing on this express reference, Sampson contends that the court failed to appreciate that cumulativeness nevertheless can be prejudicial or, at least, undervalued cumulativeness in its decisional calculus.

We begin with bedrock: the trial court, in a capital sentencing proceeding, remains free to consider cumulativeness in assessing evidentiary proffers. Cf. United States v. Barnette, 211 F.3d 803, 818-19 (4th Cir.2000) (considering quantity of victim impact evidence presented in determining whether defendant's due process rights were violated). But Sampson's contention is incorrect. The record makes manifest that the district court considered the possible prejudicial effects of cumulativeness when ruling on Sampson's evidentiary objections. There is simply no other way to explain why the court excluded a number of photographs that it thought "cumulative," "redundant," "duplicat[ive]," or "repetitive." We thus discern no error in the court's understanding of the FDPA's evidentiary standard.

A question remains as to whether the district court's decisions that the exhibits possessed probative value outweighing any associated bias were adequately supported by the record. We answer that question affirmatively. The McCloskey and Rizzo crime scene photographs and the sock used as a gag in the Rizzo murder were significantly probative of material issues; they corroborated and clarified testimony regarding the discovery of the bodies and the gathering of evidence. Similarly, the autopsy photographs shed light on the manner in which each victim was killed (an important integer in the jury's determination of whether the murders were committed in an especially heinous, cruel, or depraved manner).

Sampson stresses that the government had other means of making these points, such as by using medical examiner testimony or diagrams. It is, however, axiomatic that "the evidentiary account of what a defendant has thought and done can accomplish what no set of abstract statements ever could, not just to prove a fact but to establish its human significance." Old Chief v. United States, 519 U.S. 172, 187-88, 117 S.Ct. 644, 136 L.Ed.2d 574 (1997). Thus, within reasonable limits, the prosecution ? even in a capital case ? is entitled to present its case through the evidence it deems most appropriate. See id. Those limits were not exceeded here.

Sampson also complains that decomposition is visible in some of the photographs. While this feature obviously must be taken into account in calibrating the balance of probative value and unfairly prejudicial effect, the record makes clear that the district court gave due weight to it. Indeed, the court admitted only those photographs that "most closely depicted the condition of the victims at the time [of the killings]." Sampson IV, 335 F.Supp.2d at 183.

The upshot is that the district court's handling of gruesomeness concerns, like its handling of the crime scene and autopsy evidence generally, demonstrated a thoughtful consideration of potential prejudice. The court excluded much evidence, redacted other evidence, gave appropriate limiting instructions, and saw to it that admitted photographs were displayed circumspectly to the jury. We are left without any principled basis for finding that the court abused its discretion in regard to this evidence.13

2. The Whitney Murder. Sampson argues that the district court erred in admitting evidence of the circumstances surrounding the Whitney murder. Although he concedes that evidence of the murder itself was admissible as a non-statutory aggravating factor,14 he contends that evidence about the details of the crime (which included photographs, taped confessions, and testimony from crime scene investigators and the medical examiner) was not really relevant and, in all events, had a high potential for unfair prejudice.

We find no abuse of discretion in the admission of the Whitney evidence. The FDPA broadly provides that "[t]he government may present any information relevant to an aggravating factor for which notice has been provided." Id. Here, the government gave adequate notice that it would introduce evidence of the Whitney murder as a non-statutory aggravator, and the district court found that the evidence actually admitted would help the jury to determine how much weight it should give this factor in its sentencing calculus. The evidence made the murder more real, demonstrated the evolution of Sampson's methods, and served to rebut his claims of mental impairment and remorse.

Sampson's counter ? that the prosecution could have established the details of the Whitney murder through his confession alone ? is unavailing. After all, the prosecution is entitled to considerable latitude in deciding how to present its case. See Old Chief, 519 U.S. at 187-88, 117 S.Ct. 644. Here, moreover, the district court was assiduous in its efforts to prevent unfair prejudice; for example, it excluded all the Whitney victim impact evidence and many of the proffered photographs. It also instructed the jury about the proper role of the evidence admitted. Taking everything into account, we find the district court's judgments with respect to the Whitney evidence to be well within the encincture of its discretion.

3. Other Prosecutions. Among the compendium of mitigating factors presented to the jury, Sampson proposed to prove that numerous other federal defendants convicted of multiple murders had not been sentenced to death. In support of this mitigating factor, he sought to introduce verdict sheets and descriptive material relating to 71 other federal capital cases. The government opposed the admission of this evidence, arguing that it was irrelevant as it did not bear either on Sampson's character or record or on the circumstances of the offenses at issue. See 18 U.S.C. § 3592(a)(8). Sampson trimmed the number of proposed comparators to 47, and the district court determined that the evidence was arguably relevant in mitigation. The court then ruled, however, that the evidence's probative value was outweighed by the likelihood of juror confusion. On appeal, Sampson contests the exclusion of this evidence.

Sampson maintains, albeit in very general terms, that this evidence was relevant and that, under Tennard v. Dretke, 542 U.S. 274, 284-85, 124 S.Ct. 2562, 159 L.Ed.2d 384 (2004), a trial court may not restrict the presentation of relevant evidence offered in mitigation of a possible death sentence. This argument cannot be literally true; if it were, a capital defendant would have an unrestricted license to introduce the most confusing or misleading evidence as long as it was marginally relevant. We reject so absolutist a view. See Purkey, 428 F.3d at 756 (explaining that the FDPA's low barriers to admission of evidence in a capital sentencing hearing "do[] not mean that the defense has carte blanche to introduce any and all evidence that it wishes"); cf. Oregon v. Guzek, 546 U.S. 517, 126 S.Ct. 1226, 1232, 163 L.Ed.2d 1112 (2006) (commenting that "the Eighth Amendment does not deprive [states] of [their] authority to set reasonable limits upon the evidence a defendant can submit").

This does not end the matter, however, for it seems appropriate to construe Sampson's argument as an argument that the district court erred in balancing probative value against likelihood of juror confusion. Framing the issue in that manner brings the district court's reasoning into sharp focus. The court explained that it had found numerous omissions and inaccuracies in the case summaries that Sampson proffered and that these defects greatly diminished their probative worth. The court also found that the quantity of evidence involved would saturate the record with largely extraneous material and create a grave risk of juror confusion. The court noted:

In order to determine which of the many other cases are sufficiently similar to this case to bear on the question of proportionality, the jury would have had to hear a large amount of evidence. In effect, the court would have had to conduct many mini-trials of other FDPA cases, since a jury would be unable to perform meaningful proportionality review based on brief summaries of other cases. Rather, in order to fully appreciate the verdicts reached in those cases, jurors in this case would have had to hear substantial testimony regarding the crime and the defendant in the other cases. The amount of time that would have had to be spent educating jurors regarding all other FDPA cases in a non-prejudicial manner, which could have been measured in weeks or months, as compared to the amount of time spent on the mitigation case as a whole, likely would have diverted the jury's focus from the facts relating to Sampson and his crimes.

Sampson IV, 335 F.Supp.2d at 196.

On this chiaroscuro record, we are not disposed to substitute our judgment for that of the district court. Having supportably found that the evidence was of limited probative value and that its introduction would create a high risk of juror confusion, the district court had ample reason to exclude it. See 18 U.S.C. § 3593(c).15

4. Bank Robberies. Next, Sampson contends that the district court erred in (i) admitting evidence of the five antecedent bank robberies that he committed in North Carolina and (ii) submitting four of them to the jury as potential nonstatutory aggravating factors.16 He asserts that the bank robberies satisfy neither the requirement that an aggravating factor "genuinely narrow the class of persons eligible for the death penalty," Zant, 462 U.S. at 877, 103 S.Ct. 2733, nor the requirement that an aggravating factor rationally distinguish "those who deserve capital punishment from those who do not," Arave, 507 U.S. at 474, 113 S.Ct. 1534.

These assertions are meritless. Under the district court's instructions, four of the bank robberies served as potential non-statutory aggravating factors ? that is, as aggravating factors to be considered by the jury only after it found at least one statutory aggravating factor to be present in the case. See 18 U.S.C. § 3593(e). A non-statutory aggravating factor need only "direct the jury to the individual circumstances of the case." Jones, 527 U.S. at 402, 119 S.Ct. 2090 (plurality opinion); see also Tuilaepa, 512 U.S. at 972, 114 S.Ct. 2630 (noting "a separate requirement for the selection decision, where the sentencer determines whether a defendant eligible for the death penalty should in fact receive that sentence"). So long as it meets this requirement, a non-statutory aggravating factor ordinarily will pass constitutional muster. See Jones, 527 U.S. at 401-02, 119 S.Ct. 2090 (plurality opinion).

The four bank robberies pass muster under this standard. The government introduced evidence of the heists to demonstrate Sampson's escalating criminality immediately prior to the string of murders that he committed. Because not every capital defendant will have exhibited such a pattern, this evidence necessarily directed the jurors to the individualized circumstances of Sampson's case. Cf. id. at 402, 119 S.Ct. 2090 (finding victim impact and victim vulnerability acceptable as non-statutory factors because they were "inherently individualized"). Consequently, we hold that the district court did not abuse its discretion either in admitting evidence anent the bank robberies or in authorizing the jury to consider four of those robberies as potential non-statutory aggravating factors.

5. Spectator Reactions. Sampson's final evidentiary challenge is nontraditional in nature. It does not relate to the admission or exclusion of evidence per se but, rather, to the district court's denial of his motion for a mistrial based on the reactions of individuals in the gallery (particularly the victims' families) to certain items of evidence.

This argument is a difficult one to make. For one thing, victim-impact evidence, although inflammatory by nature, is generally admissible in the sentencing phase of a capital case. See Payne v. Tennessee, 501 U.S. 808, 827, 111 S.Ct. 2597, 115 L.Ed.2d 720 (1991). For another thing, Congress has embedded the right of victims' families to attend an accused murderer's trial in federal law. See 18 U.S.C. § 3510(b); 42 U.S.C. § 10607(e)(2)(B).

Despite these obvious obstacles, Sampson asserts that, in this case, the victims' families' ongoing reactions to the evidence presented were unfairly prejudicial. He moved for a mistrial on this ground, but the district court rebuffed his entreaty. He renews the argument in this venue.

We review the denial of a motion for a mistrial under an abuse of discretion rubric. United States v. Flecha-Maldonado, 373 F.3d 170, 177 (1st Cir.2004). In administering that standard, we keep in mind that "[a] mistrial is a last resort that is only ordered if the demonstrated harm cannot be cured by less drastic means." United States v. De Jesus Mateo, 373 F.3d 70, 72 (1st Cir.2004).

In this case, the district court exhibited great sensitivity to the volatility of the issues and took a number of steps to minimize the risk of unfair prejudice from the gallery's reactions. The court carefully instructed the jurors at the beginning of the trial that they were to decide the case based on the evidence; it cautioned that "anything you see or hear or read, even, outside of the bar that divides the lawyers and you from the public is not evidence." The court repeated this warning when the defense raised concerns about a particular juror who appeared to be watching the gallery intently, and added that the jurors "should stay focused on what's occurring inside the rail and not on the outside of the rail."

Jurors are presumed to follow instructions. See id. at 73; see also United States v. Benedetti, 433 F.3d 111, 118 (1st Cir.2005) (according substantial weight to such prophylactic instructions in evidentiary claims of unfair prejudice). The district court questioned each juror individually in response to the defense's concerns, dismissing one juror based on his replies. The court expressed "great confidence" in the rest of the jurors after thorough questioning.

The court also took a variety of other prudential measures. For example, it requested that the Rizzo family members relocate within the courtroom when a suspicion arose that they were seated in too prominent a place and that their seating might influence the jury. (Indeed, the Rizzos were relocated to an overflow room when particularly disturbing evidence was presented.)

We need not tarry. Although this was an emotion-laden trial, the district court appears to have gone the extra mile to ensure that the jury remained focused on the evidence and free from extraneous influences. Given the measures that the district court prudently took to prevent unfair prejudice, we discern no basis for a claim that the court abused its discretion in denying Sampson's motion for a mistrial.17

D. Sufficiency of the Evidence.

In addition to his specific evidentiary challenges, Sampson makes an overall claim that the evidence was insufficient to support the jury's finding of certain aggravating factors. We evaluate sufficiency challenges de novo, determining whether a rational juror could have found the disputed facts beyond a reasonable doubt. See United States v. Soler, 275 F.3d 146, 153 (1st Cir.2002). In making this determination, we consider the evidence in the light most favorable to the verdict, giving the prevailing party (here, the government) the benefit of all reasonable inferences and resolving credibility questions in its favor. See United States v. Lara, 181 F.3d 183, 200 (1st Cir.1999).

Sampson suggests that we should review the sufficiency of the evidence of especially heinous, cruel, or depraved conduct through a less deferential glass. This suggestion derives from the principle that review of this aggravator ordinarily calls for assaying the evidence in light of a narrowing construction. See Bell v. Cone, 543 U.S. 447, 453-57, 125 S.Ct. 847, 160 L.Ed.2d 881 (2005).

Sampson's suggestion dislodges the principle from its contextual underpinnings. In the case at bar, this aggravating factor was adequately narrowed by the district court's jury instructions, see supra Part III(A)(3), which incorporated the FDPA's "serious physical abuse" language. We therefore reject Sampson's attempted tweaking of the standard of review and turn to his specific challenges.

1. Especially Heinous, Cruel, or Depraved Conduct. Sampson notes that some of his post-arrest statements demonstrate an intent to kill his victims rapidly and that portions of the medical examiner testimony corroborate this intent. Building on that foundation, he contends that a rational juror could not have found that he inflicted "serious physical abuse" on McCloskey and Rizzo beyond what was necessary to end their lives. On this basis, he posits that the especially heinous, cruel, or depraved aggravating factor was not supported by the evidence.

This view of the record completely disregards the substantiality of the evidence supporting the jury's finding. With respect to McCloskey, Sampson inflicted no fewer than 24 separate stab wounds. In describing the slaying, he stated in a confession that he "didn't want to stop." He also admitted that he slit McCloskey's throat after McCloskey said that he was dying. This evidence easily supported a reasonable inference that Sampson intended to ? and did ? inflict serious physical abuse, well beyond what was necessary to kill McCloskey. Although Sampson adverts to some evidence from which the jury might have reached a different conclusion (for example, his insistence to the police that McCloskey "didn't suffer"), the jurors had both the right and the obligation to weigh all the evidence, judge the sources' veracity, and determine its significance. See United States v. Ortiz, 966 F.2d 707, 713 (1st Cir.1992). As long as "the jury's decipherment of the record represented a plausible choice among reasonable alternatives," it is deserving of respect. Id.

So, too, the jury's finding of especially heinous, cruel, or depraved conduct in relation to the Rizzo murder. Sampson first immobilized Rizzo by tying him to a tree. Although he had learned through his experience with McCloskey that slitting a victim's throat would kill swiftly, he nevertheless inflicted 15 stab wounds on Rizzo (several of which were themselves potentially fatal). At some point during the repetitive stabbing, he cut his victim's throat, severing the jugular vein and trachea. We think that this evidence, viewed in the light most favorable to the verdict, unarguably sustains a conclusion that Sampson perpetrated serious physical abuse (and thus, could be found guilty of especially heinous, cruel, or depraved conduct). See United States v. Hernández, 218 F.3d 58, 66 n. 5 (1st Cir.2000) (explaining that it is not an appellate court's role "to resolve conflicts in the evidence").

2. Vulnerability. Sampson next argues that the evidence does not support the jury's characterization of McCloskey as a particularly vulnerable victim because of the absence of any nexus between McCloskey's vulnerability and his death. This claim is unconvincing.

McCloskey's son-in-law testified that McCloskey had undergone open-heart surgery (a quintuple bypass) approximately one year prior to his encounter with Sampson; that he was overweight and became short of breath easily; and that he had difficulty walking fifteen feet shortly before his murder. Sampson's admission that he had to help McCloskey up a hill to the site of the slaying corroborated this testimony. This evidence sufficed to ground a conclusion that McCloskey was a particularly vulnerable victim, that is, that he would have had a more difficult time escaping from his assailant than the average person. See United States v. Gill, 99 F.3d 484, 486 (1st Cir.1996) (noting that the vulnerable victim federal sentencing guideline is "primarily concerned with the impaired capacity of the victim to . . . prevent the crime"). And given the circumstances of this case, McCloskey's vulnerability easily could have contributed to his death. No more was exigible. Cf. Paul, 217 F.3d at 1001-02 (holding vulnerable victim factor sufficiently supported by evidence that victim was 82 and physically unable to resist attackers).

The cases on which Sampson relies do not demand a different result. In United States v. Johnson, 136 F.Supp.2d 553 (W.D.Va.2001), the victim was killed instantly by an explosion, and the district court precluded any consideration of a vulnerable victim aggravating factor because the victim's particular vulnerability ? her pregnancy ? was not in any way related to her death. See id. at 560. In Francis v. State, 808 So.2d 110 (Fla.2001), the only evidence of vulnerability was that the otherwise healthy victims were 66 years of age. See id. at 139. Neither of these decisions is apposite here.

By like token, Sampson's reliance on McCloskey's attempts to fight back is misplaced. There is arguably some evidence of self-defense (such as the fact that McCloskey suffered several defensive wounds). However, as presented to the jury, the finding that McCloskey was a vulnerable victim could have rested on his inability to resist attack or his inability to escape. The evidence, taken in the aggregate, was sufficient to allow the jury to find that McCloskey was a particularly vulnerable victim within the purview of the FDPA. See 18 U.S.C. § 3592(c)(11).

E. New Trial Issues.

During the penalty-phase trial, Sampson attempted to prove several mitigating factors involving alleged mental illness. These included that, at the time of the killings, his "capacity to conform his conduct to the requirements of the law was significantly impaired," that he was functioning "under a severe mental or emotional disturbance," and that he was "mentally ill." No juror found that Sampson had demonstrated the existence of any of these factors by a preponderance of the evidence. Sampson now assigns error to the district court's rejection of his claims that the jurors (i) should have found in his favor on one or more of these proffered mitigating factors, and (ii) misapplied the relevant instructions.18

Since these claims were raised by way of a motion for a new trial, we review the district court's disposition of them under an abuse of discretion rubric. See United States v. George, 448 F.3d 96, 101 (1st Cir.2006); United States v. Wilkerson, 251 F.3d 273, 278 (1st Cir.2001).

1. The Mental Illness Mitigators. We start with Sampson's claim that the jury's failure to find mitigating mental illness factors was against the weight of the credible evidence.

The record contains a plethora of mental health evidence. The government called numerous witnesses who had interacted with Sampson during his week-long killing spree to demonstrate that he appeared calm, polite, and capable of normal discourse with others. The defense offered the testimony of a social worker and several prison officials to inform the jury about Sampson's behavioral patterns and mental health history. Both sides presented expert witnesses who testified about mental illness in general and Sampson's mental health in particular.

Taken as a whole, the evidence was freighted with contradictions. These contradictions, however, were grist for the jury's mill. See, e.g., Blake v. Pellegrino, 329 F.3d 43, 47-48 (1st Cir.2003). The dispositive consideration is that the record contains more than enough evidence to warrant the conclusion that Sampson's mental health need not be regarded as a mitigating factor.

There was, for example, expert testimony that Sampson suffered from an antisocial personality disorder rather than from some form of mental illness. The record likewise contains expert testimony that, during the killing spree, Sampson was not impaired in his ability to conform his conduct to the requirements of the law. The same expert vouchsafed that Sampson's crimes were not the product of mental illness, emotional distress, or drug use. The government supplemented and supported this testimony through lay testimony, medical and psychiatric records, Sampson's own statements, and effective cross-examination of defense witnesses. In the end, a jury reasonably could have concluded ? as this jury did ? that Sampson did not suffer from any mental impairments sufficient to mitigate any need for the imposition of a death sentence.

Sampson accurately notes that the district court expressed some disagreement with the jury on this point. But the district court parted ways with the jury only on a relatively narrow issue: whether Sampson suffered from bipolar disorder (the court indicated that it found the defense's expert more persuasive than the government's expert on this point). The jury was entitled to find otherwise. See Ortiz, 966 F.2d at 713.

To cinch matters, the district court, after expressing its opinion, stated clearly that it "d[id] not . . . find that the evidence on this issue predominate[d] heavily in favor of the defendant being found to be bipolar" and that, therefore, "it [would] not [be] appropriate for the court to disregard the jury's decision on the mitigating factor of mental illness." Sampson III, 332 F.Supp.2d at 331. In light of that finding ? which is borne out by the record ? the district court had no choice but to honor the jury's determination. See United States v. Rothrock, 806 F.2d 318, 322 (1st Cir.1986) (emphasizing that a trial judge "is not a thirteenth juror" and may not "set aside a verdict merely because he would have reached a different result"). Like the district court, we too reject Sampson's challenge to the jury's mental illness findings.

2. Post-Trial Juror Statements. We turn next to a related matter. A week or so after the jury returned its verdict, a local newspaper quoted a juror to the effect that Sampson's ability to "know[] the difference between right and wrong" was the "fulcrum on which everything else balanced." In a separate account, the same juror reportedly stated that Sampson "knew right from wrong."

Sampson interpreted these statements as evidence that the jury had misapplied the court's "mental illness" instructions, which explained that no one had argued that Sampson "was completely unable to conform his conduct to the requirements of the law." Based on this suspected misapplication, Sampson moved for a new trial or, in the alternative, an evidentiary hearing. The district court turned him down, reasoning in part that post-trial juror statements could not be used to impeach a verdict. See Fed.R.Evid. 606(b). Sampson now assigns error.

Rule 606(b) provides in pertinent part that, after a jury has returned its verdict, juror statements may not be considered "as to any matter . . . occurring during the course of the jury's deliberations or to the effect of anything upon that or any other juror's mind . . . or concerning the juror's mental processes in connection therewith." The statements upon which Sampson relies ordinarily would fall squarely within this prohibition: they concern the jurors' evaluation of the mental health evidence and the weight that they chose to attach to that evidence.

Although conceding that Rule 606(b) would bar the statements under most circumstances, Sampson asseverates that they nevertheless should be admitted because, in capital sentencing proceedings, the FDPA displaces the Federal Rules of Evidence. His fallback position is that the heightened interest in the reliability of capital sentencing determinations trumps Rule 606(b).

We need not decide the issue. Even if we assume, purely for argument's sake, that the juror's statements should have been taken into consideration, any error would have been manifestly harmless. In that regard, we concur with the district court's alternate holding that the statements do not indicate that the jury necessarily misunderstood the court's instructions on mental illness. Given the reference to a "fulcrum on which everything else balanced," the juror's statements easily can be construed as referring to the weighing decision rather than the special findings regarding the mental illness mitigators. Thus, there was no abuse of discretion in the district court's refusal to grant either a new trial or an evidentiary hearing based on Sampson's objections to the jury's mental illness findings.

F. Cumulative Error.

Sampson's penultimate claim is that the errors of which he complains, even if not mandating reversal when considered separately, collectively require that his sentence be vacated. We do not dispute the legal premise on which this argument rests: "a column of errors may sometimes have a logarithmic effect, producing a total impact greater than the arithmetic sum of its constituent parts." United States v. Sepulveda, 15 F.3d 1161, 1196 (1st Cir. 1993). Here, however, the district court handled the case patiently and sensitively. None of its individual rulings worked any cognizable harm to Sampson's rights. It necessarily follows that the cumulative error doctrine finds no foothold in this appeal.

IV. ARBITRARINESS

In the final chapter of this appeal, we must independently evaluate, as required by the FDPA, "whether the sentence of death was imposed under the influence of passion, prejudice, or any other arbitrary factor." 18 U.S.C. § 3595(c)(1). Having assiduously performed that examination, we find no sign that any such factors contributed to Sampson's sentence.

The results of the jury's deliberations fully support this conclusion. In addition to finding the aggravating factors that we have discussed, the jurors failed to find other aggravating factors suggested by the government. Moreover, the jurors found several mitigating factors. Viewed collectively, these findings suggest that the jury considered the evidence in a thorough, even-handed, and dispassionate manner. Cf. Paul, 217 F.3d at 1004-05 (finding no arbitrariness when the jury followed "exactly the process [it] was to complete").

V. CONCLUSION

We need go no further. For the reasons elucidated above, we reject Sampson's principal assignments of error. To the extent that he has raised other claims of error, none requires discussion, and we reject them out of hand.

We add only that Sampson has been ably represented by learned counsel. His positions have been vigorously asserted. While we are aware that death is the ultimate punishment, we are persuaded that the sentencing proceedings in this case were conducted fairly and with scrupulous attention to the process required by law. Accordingly, we affirm the sentence of death.

Affirmed.

In addition, Sampson argues that this court should invoke its supervisory powers "to curb charging discrimination and regional caprice." Appellant's Br. at 275-76. There is no basis for the exercise of supervisory power in this instance. If Sampson's arguments have any basis in fact-a point upon which we do not opine-he could only have benefitted by virtue of his race and the geographic location in which his crimes were committed.

5 InMcCleskey, the Supreme Court rejected a capital defendant's claim that systemic statistics demonstrated discriminatory intent in his particular case. See 481 U.S. at 297, 107 S.Ct. 1756. Sampson attempts to distinguish McCleskey by noting that the DOJ study on which he relies provides not only systemic statistics but also individualized statistics. He points out that while the study at issue in McCleskey analyzed data from many different decisionmakers, the DOJ study relies only on the decisions of the Attorney General and primarily on the decisions of one Attorney General (Janet Reno). This argument ignores the fact that the statistics also reflect the decisions of countless prosecutors in the field, who must exercise their considerable charging discretion before a case ever reaches the Attorney General's desk (as Sampson points out, the Attorney General followed the local prosecutors' recommendations in the overwhelming majority of cases submitted, Appellant's Br. at 255 n. 90). See McCleskey, 481 U.S. at 295 n. 15, 107 S.Ct. 1756 (noting that "decisions whether to prosecute and what to charge necessarily are individualized and involve infinite factual variations").

6 To the extent that Sampson invokes the Eighth Amendment, arguing that the risk of executing the innocent renders the federal death penalty per se cruel and unusual, his claim is foreclosed byGregg. See 428 U.S. at 187, 96 S.Ct. 2909 (opinion of Stewart, Powell, and Stevens, JJ.); id. at 226, 96 S.Ct. 2909 (opinion of White, J., joined by Burger, C.J., and Rehnquist, J.); see also Marsh, 126 S.Ct. at 2529 (rejecting the proposition that "the death penalty can only be just in a system that does not permit error").

7 That section provides, in pertinent part, that if the jury finds the existence of at least one of the relevant aggravating factors enumerated in the statute, "the jury . . . shall consider whether all the aggravating factor or factors found to exist sufficiently outweigh all the mitigating factor or factors found to exist to justify a sentence of death." 18 U.S.C. § 3593(e)

8 Sampson urges us to apply, instead ofBoyde, either the standard formulated by the Supreme Court in Mills v. Maryland, 486 U.S. 367, 377, 108 S.Ct. 1860, 100 L.Ed.2d 384 (1988), or that announced in Stromberg v. California, 283 U.S. 359, 367-68, 51 S.Ct. 532, 75 L.Ed. 1117 (1931). Mills is obsolete; the Supreme Court reformulated that standard in Boyde, 494 U.S. at 378-90, 110 S.Ct. 1190. Stromberg is inapposite. There, the Court stated that when a jury is instructed on alternative theories, one of which is plainly unconstitutional, a conviction based upon a general verdict must be set aside. 283 U.S. at 367-68, 51 S.Ct. 532. But this principle applies only where an instruction is "concededly erroneous." Boyde, 494 U.S. at 380, 110 S.Ct. 1190. For this reason, and because the verdict sheets in this case provide detailed evidence of the jury's decisional calculus, Stromberg is not on point.

9 In contemplating its instructions to the jury, the district court appears to have distinguished between applying the reasonable doubt standard to the decision about whether aggravators outweigh mitigators and applying the standard to the jury's ultimate decision on the appropriateness of a capital sentenceSee Sampson IV, 335 F.Supp.2d at 234-40. We already have held that the reasonable doubt standard is not required in the weighing of aggravators against mitigators. See text supra. There is no challenge on appeal to the correctness of the district court's application of the reasonable doubt standard to the jury's ultimate sentencing decision and, in all events, any error in this regard would have favored Sampson and, thus, would have been harmless. Consequently, we take no view of the propriety of the distinction drawn by the district court.

10 One member of the panel joins this conclusion on a limited basis. Although Judge Lipez concludes that no constitutional error occurred in this case with respect to use of the vulnerable victim factor, he has reservations about the use of the factor, without scienter, as the sole aggravating factor making a defendant eligible for the death penalty. Given that Sampson was found eligible in connection with the McCloskey murder based on an additional factor (that the crime was committed in "an especially heinous, cruel, or depraved manner") and that the evidence showed that Sampson must have been aware of McCloskey's infirmities,see infra Part III(D)(2), the outcome here is consistent with his views.

11 While the district court's instruction unquestionably provided the constitutionally-mandated narrowing, we do not hold that the limiting construction here is the only one that would be constitutionally permissible. We leave open the question of whether a broader definition of serious physical abuse might still pass constitutional muster

12 Rule 403 provides in pertinent part that "evidence may be excluded if its probative value is substantially outweighed by the danger of unfair prejudice, confusion of the issues, or misleading the jury, or by considerations of undue delay, waste of time, or needless presentation of cumulative evidence."

13 Although several of the photographs to which Sampson now objects were not challenged in the district court, we need not filter them through the plain error screen. It suffices to say that there was no abuse of discretion in the district court's admission of these photographs

14 The term "non-statutory aggravating factor" is used to "refer to any aggravating factor that is not specifically described in 18 U.S.C. § 3592."Jones, 527 U.S. at 377 n. 2, 119 S.Ct. 2090. While only the finding of a statutory aggravating factor can render a defendant death-eligible, the jury may consider non-statutory aggravating factors in deciding whether a sentence of death is appropriate. See 18 U.S.C. § 3593(c)-(e).

15 This determination renders it unnecessary for us to address the government's alternate argument that this evidence did not in any event qualify as mitigating evidence

16 Based on testimony that Sampson did not have a weapon during one of the robberies, the district court ultimately submitted only four of the robberies to the jury as potential aggravators. Sampson makes no specific complaint about the singular handling of the fifth (unarmed) robbery, which the court instructed the jury to disregard

17 Sampson's invocation, by way of Federal Rule of Appellate Procedure 28(j), of the concurrences inCarey v. Musladin, ___ U.S. ___, 127 S.Ct. 649, 654-58, 166 L.Ed.2d 482 (2006) (Stevens, Kennedy, and Souter, JJ., concurring), does not alter our analysis. He cites the statements contained therein as indicia of the Supreme Court's concerns over the potential for improper influence represented by the conduct of spectators. However, these concurrences focus on the impact that affirmative demonstrations by spectators (there, the wearing of buttons by spectators that featured an image of the victim) may have during the guilt phase of a trial. The claim here is of a materially different character: the families' reactions to Sampson's crimes are a natural by-product of relevant evidence properly introduced during the sentencing phase.

18 Sampson's quest for a new trial also included a claim that the jury exhibited unfair prejudice due to a so-called "white victim" effect. What we have written earlier,see supra Part II(C)(1), fully disposes of the claim that the district court erred in denying this aspect of Sampson's motion for a new trial.